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<div class="title">BesselFunctionsImpl.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2015 Eugene Brevdo &lt;ebrevdo@gmail.com&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160; </div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="preprocessor">#ifndef EIGEN_BESSEL_FUNCTIONS_H</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#define EIGEN_BESSEL_FUNCTIONS_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160; </div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160; </div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160; </div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="comment">//  Parts of this code are based on the Cephes Math Library.</span></div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="comment">//  Cephes Math Library Release 2.8:  June, 2000</span></div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="comment">//  Copyright 1984, 1987, 1992, 2000 by Stephen L. Moshier</span></div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="comment">//  Permission has been kindly provided by the original author</span></div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="comment">//  to incorporate the Cephes software into the Eigen codebase:</span></div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="comment">//    From: Stephen Moshier</span></div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;<span class="comment">//    To: Eugene Brevdo</span></div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="comment">//    Subject: Re: Permission to wrap several cephes functions in Eigen</span></div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="comment">//    Hello Eugene,</span></div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;<span class="comment">//    Thank you for writing.</span></div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;<span class="comment">//    If your licensing is similar to BSD, the formal way that has been</span></div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;<span class="comment">//    handled is simply to add a statement to the effect that you are incorporating</span></div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;<span class="comment">//    the Cephes software by permission of the author.</span></div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;<span class="comment">//    Good luck with your project,</span></div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;<span class="comment">//    Steve</span></div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160; </div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160; </div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;<span class="comment">/****************************************************************************</span></div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;<span class="comment"> * Implementation of Bessel function, based on Cephes                       *</span></div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;<span class="comment"> ****************************************************************************/</span></div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160; </div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar&gt;</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;<span class="keyword">struct </span>bessel_i0e_retval {</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;  <span class="keyword">typedef</span> Scalar type;</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;};</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160; </div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;template &lt;typename T, typename ScalarType = typename unpacket_traits&lt;T&gt;::type&gt;</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;<span class="keyword">struct </span>generic_i0e {</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;  EIGEN_STATIC_ASSERT((internal::is_same&lt;T, T&gt;::value == <span class="keyword">false</span>),</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;                      THIS_TYPE_IS_NOT_SUPPORTED)</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160; </div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;  EIGEN_DEVICE_FUNC <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp;) {</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;    <span class="keywordflow">return</span> ScalarType(0);</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;  }</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;};</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160; </div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;<span class="keyword">struct </span>generic_i0e&lt;T, float&gt; {</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp; x) {</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;    <span class="comment">/*  i0ef.c</span></div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;<span class="comment">     *  Modified Bessel function of order zero,</span></div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;<span class="comment">     *  exponentially scaled</span></div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;<span class="comment">     * SYNOPSIS:</span></div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;<span class="comment">     * float x, y, i0ef();</span></div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;<span class="comment">     * y = i0ef( x );</span></div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;<span class="comment">     * DESCRIPTION:</span></div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;<span class="comment">     * Returns exponentially scaled modified Bessel function</span></div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;<span class="comment">     * of order zero of the argument.</span></div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;<span class="comment">     * The function is defined as i0e(x) = exp(-|x|) j0( ix ).</span></div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;<span class="comment">     * ACCURACY:</span></div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;<span class="comment">     *                      Relative error:</span></div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;<span class="comment">     * arithmetic   domain     # trials      peak         rms</span></div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;<span class="comment">     *    IEEE      0,30        100000      3.7e-7      7.0e-8</span></div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;<span class="comment">     * See i0f().</span></div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;<span class="comment">     */</span></div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160; </div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> A[] = {-1.30002500998624804212E-8f, 6.04699502254191894932E-8f,</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;                       -2.67079385394061173391E-7f, 1.11738753912010371815E-6f,</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;                       -4.41673835845875056359E-6f, 1.64484480707288970893E-5f,</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;                       -5.75419501008210370398E-5f, 1.88502885095841655729E-4f,</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;                       -5.76375574538582365885E-4f, 1.63947561694133579842E-3f,</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;                       -4.32430999505057594430E-3f, 1.05464603945949983183E-2f,</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;                       -2.37374148058994688156E-2f, 4.93052842396707084878E-2f,</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;                       -9.49010970480476444210E-2f, 1.71620901522208775349E-1f,</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;                       -3.04682672343198398683E-1f, 6.76795274409476084995E-1f};</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160; </div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> B[] = {3.39623202570838634515E-9f, 2.26666899049817806459E-8f,</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;                       2.04891858946906374183E-7f, 2.89137052083475648297E-6f,</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;                       6.88975834691682398426E-5f, 3.36911647825569408990E-3f,</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;                       8.04490411014108831608E-1f};</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;    T y = pabs(x);</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;    T y_le_eight = internal::pchebevl&lt;T, 18&gt;::run(</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;        pmadd(pset1&lt;T&gt;(0.5f), y, pset1&lt;T&gt;(-2.0f)), A);</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;    T y_gt_eight = pmul(</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;        internal::pchebevl&lt;T, 7&gt;::run(</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;            psub(pdiv(pset1&lt;T&gt;(32.0f), y), pset1&lt;T&gt;(2.0f)), B),</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;        prsqrt(y));</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;    <span class="comment">// TODO: Perhaps instead check whether all packet elements are in</span></div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;    <span class="comment">// [-8, 8] and evaluate a branch based off of that. It&#39;s possible</span></div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;    <span class="comment">// in practice most elements are in this region.</span></div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;    <span class="keywordflow">return</span> pselect(pcmp_le(y, pset1&lt;T&gt;(8.0f)), y_le_eight, y_gt_eight);</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;  }</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;};</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160; </div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;<span class="keyword">struct </span>generic_i0e&lt;T, double&gt; {</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp; x) {</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;    <span class="comment">/*  i0e.c</span></div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;<span class="comment">     *  Modified Bessel function of order zero,</span></div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;<span class="comment">     *  exponentially scaled</span></div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;<span class="comment">     * SYNOPSIS:</span></div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;<span class="comment">     * double x, y, i0e();</span></div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;<span class="comment">     * y = i0e( x );</span></div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;<span class="comment">     * DESCRIPTION:</span></div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;<span class="comment">     * Returns exponentially scaled modified Bessel function</span></div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;<span class="comment">     * of order zero of the argument.</span></div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;<span class="comment">     * The function is defined as i0e(x) = exp(-|x|) j0( ix ).</span></div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;<span class="comment">     * ACCURACY:</span></div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;<span class="comment">     *                      Relative error:</span></div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;<span class="comment">     * arithmetic   domain     # trials      peak         rms</span></div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;<span class="comment">     *    IEEE      0,30        30000       5.4e-16     1.2e-16</span></div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;<span class="comment">     * See i0().</span></div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;<span class="comment">     */</span></div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160; </div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> A[] = {-4.41534164647933937950E-18, 3.33079451882223809783E-17,</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;                        -2.43127984654795469359E-16, 1.71539128555513303061E-15,</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;                        -1.16853328779934516808E-14, 7.67618549860493561688E-14,</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;                        -4.85644678311192946090E-13, 2.95505266312963983461E-12,</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;                        -1.72682629144155570723E-11, 9.67580903537323691224E-11,</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;                        -5.18979560163526290666E-10, 2.65982372468238665035E-9,</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;                        -1.30002500998624804212E-8,  6.04699502254191894932E-8,</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;                        -2.67079385394061173391E-7,  1.11738753912010371815E-6,</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;                        -4.41673835845875056359E-6,  1.64484480707288970893E-5,</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;                        -5.75419501008210370398E-5,  1.88502885095841655729E-4,</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;                        -5.76375574538582365885E-4,  1.63947561694133579842E-3,</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;                        -4.32430999505057594430E-3,  1.05464603945949983183E-2,</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;                        -2.37374148058994688156E-2,  4.93052842396707084878E-2,</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;                        -9.49010970480476444210E-2,  1.71620901522208775349E-1,</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;                        -3.04682672343198398683E-1,  6.76795274409476084995E-1};</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> B[] = {</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;        -7.23318048787475395456E-18, -4.83050448594418207126E-18,</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;        4.46562142029675999901E-17,  3.46122286769746109310E-17,</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;        -2.82762398051658348494E-16, -3.42548561967721913462E-16,</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;        1.77256013305652638360E-15,  3.81168066935262242075E-15,</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;        -9.55484669882830764870E-15, -4.15056934728722208663E-14,</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;        1.54008621752140982691E-14,  3.85277838274214270114E-13,</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;        7.18012445138366623367E-13,  -1.79417853150680611778E-12,</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;        -1.32158118404477131188E-11, -3.14991652796324136454E-11,</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;        1.18891471078464383424E-11,  4.94060238822496958910E-10,</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;        3.39623202570838634515E-9,   2.26666899049817806459E-8,</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;        2.04891858946906374183E-7,   2.89137052083475648297E-6,</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;        6.88975834691682398426E-5,   3.36911647825569408990E-3,</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;        8.04490411014108831608E-1};</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;    T y = pabs(x);</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;    T y_le_eight = internal::pchebevl&lt;T, 30&gt;::run(</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;        pmadd(pset1&lt;T&gt;(0.5), y, pset1&lt;T&gt;(-2.0)), A);</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;    T y_gt_eight = pmul(</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;        internal::pchebevl&lt;T, 25&gt;::run(</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;            psub(pdiv(pset1&lt;T&gt;(32.0), y), pset1&lt;T&gt;(2.0)), B),</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;        prsqrt(y));</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;    <span class="comment">// TODO: Perhaps instead check whether all packet elements are in</span></div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;    <span class="comment">// [-8, 8] and evaluate a branch based off of that. It&#39;s possible</span></div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;    <span class="comment">// in practice most elements are in this region.</span></div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;    <span class="keywordflow">return</span> pselect(pcmp_le(y, pset1&lt;T&gt;(8.0)), y_le_eight, y_gt_eight);</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;  }</div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;};</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160; </div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;<span class="keyword">struct </span>bessel_i0e_impl {</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T x) {</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;    <span class="keywordflow">return</span> generic_i0e&lt;T&gt;::run(x);</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;  }</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;};</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160; </div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar&gt;</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;<span class="keyword">struct </span>bessel_i0_retval {</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;  <span class="keyword">typedef</span> Scalar type;</div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;};</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160; </div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;template &lt;typename T, typename ScalarType = typename unpacket_traits&lt;T&gt;::type&gt;</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;<span class="keyword">struct </span>generic_i0 {</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp; x) {</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;    <span class="keywordflow">return</span> pmul(</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;        pexp(pabs(x)),</div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;        generic_i0e&lt;T, ScalarType&gt;::run(x));</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;  }</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;};</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160; </div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;<span class="keyword">struct </span>bessel_i0_impl {</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T x) {</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;    <span class="keywordflow">return</span> generic_i0&lt;T&gt;::run(x);</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;  }</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;};</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160; </div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar&gt;</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;<span class="keyword">struct </span>bessel_i1e_retval {</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;  <span class="keyword">typedef</span> Scalar type;</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;};</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160; </div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;template &lt;typename T, typename ScalarType = typename unpacket_traits&lt;T&gt;::type &gt;</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;<span class="keyword">struct </span>generic_i1e {</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;  EIGEN_STATIC_ASSERT((internal::is_same&lt;T, T&gt;::value == <span class="keyword">false</span>),</div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;                      THIS_TYPE_IS_NOT_SUPPORTED)</div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160; </div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;  EIGEN_DEVICE_FUNC <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp;) {</div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;    <span class="keywordflow">return</span> ScalarType(0);</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;  }</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;};</div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160; </div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;<span class="keyword">struct </span>generic_i1e&lt;T, float&gt; {</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp; x) {</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;    <span class="comment">/* i1ef.c</span></div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;<span class="comment">     *  Modified Bessel function of order one,</span></div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;<span class="comment">     *  exponentially scaled</span></div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;<span class="comment">     * SYNOPSIS:</span></div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;<span class="comment">     * float x, y, i1ef();</span></div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;<span class="comment">     * y = i1ef( x );</span></div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;<span class="comment">     * DESCRIPTION:</span></div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;<span class="comment">     * Returns exponentially scaled modified Bessel function</span></div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;<span class="comment">     * of order one of the argument.</span></div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;<span class="comment">     * The function is defined as i1(x) = -i exp(-|x|) j1( ix ).</span></div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;<span class="comment">     * ACCURACY:</span></div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;<span class="comment">     *                      Relative error:</span></div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;<span class="comment">     * arithmetic   domain     # trials      peak         rms</span></div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;<span class="comment">     *    IEEE      0, 30       30000       1.5e-6      1.5e-7</span></div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;<span class="comment">     * See i1().</span></div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;<span class="comment">     */</span></div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> A[] = {9.38153738649577178388E-9f, -4.44505912879632808065E-8f,</div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;                       2.00329475355213526229E-7f, -8.56872026469545474066E-7f,</div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;                       3.47025130813767847674E-6f, -1.32731636560394358279E-5f,</div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;                       4.78156510755005422638E-5f, -1.61760815825896745588E-4f,</div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;                       5.12285956168575772895E-4f, -1.51357245063125314899E-3f,</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;                       4.15642294431288815669E-3f, -1.05640848946261981558E-2f,</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;                       2.47264490306265168283E-2f, -5.29459812080949914269E-2f,</div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;                       1.02643658689847095384E-1f, -1.76416518357834055153E-1f,</div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;                       2.52587186443633654823E-1f};</div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160; </div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> B[] = {-3.83538038596423702205E-9f, -2.63146884688951950684E-8f,</div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;                       -2.51223623787020892529E-7f, -3.88256480887769039346E-6f,</div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;                       -1.10588938762623716291E-4f, -9.76109749136146840777E-3f,</div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;                       7.78576235018280120474E-1f};</div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160; </div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160; </div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;    T y = pabs(x);</div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;    T y_le_eight = pmul(y, internal::pchebevl&lt;T, 17&gt;::run(</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;        pmadd(pset1&lt;T&gt;(0.5f), y, pset1&lt;T&gt;(-2.0f)), A));</div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;    T y_gt_eight = pmul(</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;        internal::pchebevl&lt;T, 7&gt;::run(</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;            psub(pdiv(pset1&lt;T&gt;(32.0f), y),</div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;                 pset1&lt;T&gt;(2.0f)), B),</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;        prsqrt(y));</div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;    <span class="comment">// TODO: Perhaps instead check whether all packet elements are in</span></div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;    <span class="comment">// [-8, 8] and evaluate a branch based off of that. It&#39;s possible</span></div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;    <span class="comment">// in practice most elements are in this region.</span></div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;    y = pselect(pcmp_le(y, pset1&lt;T&gt;(8.0f)), y_le_eight, y_gt_eight);</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;    <span class="keywordflow">return</span> pselect(pcmp_lt(x, pset1&lt;T&gt;(0.0f)), pnegate(y), y);</div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;  }</div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;};</div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160; </div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;<span class="keyword">struct </span>generic_i1e&lt;T, double&gt; {</div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp; x) {</div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;    <span class="comment">/*  i1e.c</span></div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;<span class="comment">     *  Modified Bessel function of order one,</span></div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;<span class="comment">     *  exponentially scaled</span></div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;<span class="comment">     * SYNOPSIS:</span></div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;<span class="comment">     * double x, y, i1e();</span></div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;<span class="comment">     * y = i1e( x );</span></div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;<span class="comment">     * DESCRIPTION:</span></div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;<span class="comment">     * Returns exponentially scaled modified Bessel function</span></div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;<span class="comment">     * of order one of the argument.</span></div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;<span class="comment">     * The function is defined as i1(x) = -i exp(-|x|) j1( ix ).</span></div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;<span class="comment">     * ACCURACY:</span></div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;<span class="comment">     *                      Relative error:</span></div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;<span class="comment">     * arithmetic   domain     # trials      peak         rms</span></div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;<span class="comment">     *    IEEE      0, 30       30000       2.0e-15     2.0e-16</span></div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;<span class="comment">     * See i1().</span></div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;<span class="comment">     */</span></div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> A[] = {2.77791411276104639959E-18, -2.11142121435816608115E-17,</div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;                        1.55363195773620046921E-16, -1.10559694773538630805E-15,</div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;                        7.60068429473540693410E-15, -5.04218550472791168711E-14,</div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;                        3.22379336594557470981E-13, -1.98397439776494371520E-12,</div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;                        1.17361862988909016308E-11, -6.66348972350202774223E-11,</div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;                        3.62559028155211703701E-10, -1.88724975172282928790E-9,</div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;                        9.38153738649577178388E-9,  -4.44505912879632808065E-8,</div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;                        2.00329475355213526229E-7,  -8.56872026469545474066E-7,</div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;                        3.47025130813767847674E-6,  -1.32731636560394358279E-5,</div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;                        4.78156510755005422638E-5,  -1.61760815825896745588E-4,</div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;                        5.12285956168575772895E-4,  -1.51357245063125314899E-3,</div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;                        4.15642294431288815669E-3,  -1.05640848946261981558E-2,</div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;                        2.47264490306265168283E-2,  -5.29459812080949914269E-2,</div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;                        1.02643658689847095384E-1,  -1.76416518357834055153E-1,</div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;                        2.52587186443633654823E-1};</div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> B[] = {</div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;        7.51729631084210481353E-18,  4.41434832307170791151E-18,</div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;        -4.65030536848935832153E-17, -3.20952592199342395980E-17,</div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;        2.96262899764595013876E-16,  3.30820231092092828324E-16,</div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;        -1.88035477551078244854E-15, -3.81440307243700780478E-15,</div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;        1.04202769841288027642E-14,  4.27244001671195135429E-14,</div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;        -2.10154184277266431302E-14, -4.08355111109219731823E-13,</div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;        -7.19855177624590851209E-13, 2.03562854414708950722E-12,</div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;        1.41258074366137813316E-11,  3.25260358301548823856E-11,</div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;        -1.89749581235054123450E-11, -5.58974346219658380687E-10,</div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;        -3.83538038596423702205E-9,  -2.63146884688951950684E-8,</div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;        -2.51223623787020892529E-7,  -3.88256480887769039346E-6,</div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;        -1.10588938762623716291E-4,  -9.76109749136146840777E-3,</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;        7.78576235018280120474E-1};</div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;    T y = pabs(x);</div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;    T y_le_eight = pmul(y, internal::pchebevl&lt;T, 29&gt;::run(</div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;        pmadd(pset1&lt;T&gt;(0.5), y, pset1&lt;T&gt;(-2.0)), A));</div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;    T y_gt_eight = pmul(</div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;        internal::pchebevl&lt;T, 25&gt;::run(</div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;            psub(pdiv(pset1&lt;T&gt;(32.0), y),</div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;                 pset1&lt;T&gt;(2.0)), B),</div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;        prsqrt(y));</div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;    <span class="comment">// TODO: Perhaps instead check whether all packet elements are in</span></div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;    <span class="comment">// [-8, 8] and evaluate a branch based off of that. It&#39;s possible</span></div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;    <span class="comment">// in practice most elements are in this region.</span></div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;    y = pselect(pcmp_le(y, pset1&lt;T&gt;(8.0)), y_le_eight, y_gt_eight);</div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;    <span class="keywordflow">return</span> pselect(pcmp_lt(x, pset1&lt;T&gt;(0.0)), pnegate(y), y);</div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;  }</div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;};</div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160; </div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;<span class="keyword">struct </span>bessel_i1e_impl {</div>
<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T x) {</div>
<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;    <span class="keywordflow">return</span> generic_i1e&lt;T&gt;::run(x);</div>
<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;  }</div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;};</div>
<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160; </div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;<span class="keyword">struct </span>bessel_i1_retval {</div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;  <span class="keyword">typedef</span> T type;</div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;};</div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160; </div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;template &lt;typename T, typename ScalarType = typename unpacket_traits&lt;T&gt;::type&gt;</div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;<span class="keyword">struct </span>generic_i1 {</div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp; x) {</div>
<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;    <span class="keywordflow">return</span> pmul(</div>
<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;        pexp(pabs(x)),</div>
<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;        generic_i1e&lt;T, ScalarType&gt;::run(x));</div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;  }</div>
<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;};</div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160; </div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;<span class="keyword">struct </span>bessel_i1_impl {</div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T x) {</div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;    <span class="keywordflow">return</span> generic_i1&lt;T&gt;::run(x);</div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;  }</div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;};</div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160; </div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;<span class="keyword">struct </span>bessel_k0e_retval {</div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;  <span class="keyword">typedef</span> T type;</div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160;};</div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160; </div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;template &lt;typename T, typename ScalarType = typename unpacket_traits&lt;T&gt;::type&gt;</div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;<span class="keyword">struct </span>generic_k0e {</div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;  EIGEN_STATIC_ASSERT((internal::is_same&lt;T, T&gt;::value == <span class="keyword">false</span>),</div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;                      THIS_TYPE_IS_NOT_SUPPORTED)</div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160; </div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;  EIGEN_DEVICE_FUNC <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp;) {</div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;    <span class="keywordflow">return</span> ScalarType(0);</div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;  }</div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;};</div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160; </div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;<span class="keyword">struct </span>generic_k0e&lt;T, float&gt; {</div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp; x) {</div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;    <span class="comment">/*  k0ef.c</span></div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;<span class="comment">     *  Modified Bessel function, third kind, order zero,</span></div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;<span class="comment">     *  exponentially scaled</span></div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160;<span class="comment">     * SYNOPSIS:</span></div>
<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;<span class="comment">     * float x, y, k0ef();</span></div>
<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;<span class="comment">     * y = k0ef( x );</span></div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;<span class="comment">     * DESCRIPTION:</span></div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;<span class="comment">     * Returns exponentially scaled modified Bessel function</span></div>
<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160;<span class="comment">     * of the third kind of order zero of the argument.</span></div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;<span class="comment">     * ACCURACY:</span></div>
<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160;<span class="comment">     *                      Relative error:</span></div>
<div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160;<span class="comment">     * arithmetic   domain     # trials      peak         rms</span></div>
<div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;<span class="comment">     *    IEEE      0, 30       30000       8.1e-7      7.8e-8</span></div>
<div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;<span class="comment">     * See k0().</span></div>
<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;<span class="comment">     */</span></div>
<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160; </div>
<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> A[] = {1.90451637722020886025E-9f, 2.53479107902614945675E-7f,</div>
<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;                       2.28621210311945178607E-5f, 1.26461541144692592338E-3f,</div>
<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;                       3.59799365153615016266E-2f, 3.44289899924628486886E-1f,</div>
<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;                       -5.35327393233902768720E-1f};</div>
<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160; </div>
<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> B[] = {-1.69753450938905987466E-9f, 8.57403401741422608519E-9f,</div>
<div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;                       -4.66048989768794782956E-8f, 2.76681363944501510342E-7f,</div>
<div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;                       -1.83175552271911948767E-6f, 1.39498137188764993662E-5f,</div>
<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160;                       -1.28495495816278026384E-4f, 1.56988388573005337491E-3f,</div>
<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;                       -3.14481013119645005427E-2f, 2.44030308206595545468E0f};</div>
<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160;    <span class="keyword">const</span> T MAXNUM = pset1&lt;T&gt;(NumTraits&lt;float&gt;::infinity());</div>
<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;    <span class="keyword">const</span> T two = pset1&lt;T&gt;(2.0);</div>
<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160;    T x_le_two = internal::pchebevl&lt;T, 7&gt;::run(</div>
<div class="line"><a name="l00494"></a><span class="lineno">  494</span>&#160;        pmadd(x, x, pset1&lt;T&gt;(-2.0)), A);</div>
<div class="line"><a name="l00495"></a><span class="lineno">  495</span>&#160;    x_le_two = pmadd(</div>
<div class="line"><a name="l00496"></a><span class="lineno">  496</span>&#160;        generic_i0&lt;T, float&gt;::run(x), pnegate(</div>
<div class="line"><a name="l00497"></a><span class="lineno">  497</span>&#160;            plog(pmul(pset1&lt;T&gt;(0.5), x))), x_le_two);</div>
<div class="line"><a name="l00498"></a><span class="lineno">  498</span>&#160;    x_le_two = pmul(pexp(x), x_le_two);</div>
<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160;    T x_gt_two = pmul(</div>
<div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160;            internal::pchebevl&lt;T, 10&gt;::run(</div>
<div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160;                psub(pdiv(pset1&lt;T&gt;(8.0), x), two), B),</div>
<div class="line"><a name="l00502"></a><span class="lineno">  502</span>&#160;            prsqrt(x));</div>
<div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160;    <span class="keywordflow">return</span> pselect(</div>
<div class="line"><a name="l00504"></a><span class="lineno">  504</span>&#160;        pcmp_le(x, pset1&lt;T&gt;(0.0)),</div>
<div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160;        MAXNUM,</div>
<div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160;        pselect(pcmp_le(x, two), x_le_two, x_gt_two));</div>
<div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160;  }</div>
<div class="line"><a name="l00508"></a><span class="lineno">  508</span>&#160;};</div>
<div class="line"><a name="l00509"></a><span class="lineno">  509</span>&#160; </div>
<div class="line"><a name="l00510"></a><span class="lineno">  510</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00511"></a><span class="lineno">  511</span>&#160;<span class="keyword">struct </span>generic_k0e&lt;T, double&gt; {</div>
<div class="line"><a name="l00512"></a><span class="lineno">  512</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp; x) {</div>
<div class="line"><a name="l00514"></a><span class="lineno">  514</span>&#160;    <span class="comment">/*  k0e.c</span></div>
<div class="line"><a name="l00515"></a><span class="lineno">  515</span>&#160;<span class="comment">     *  Modified Bessel function, third kind, order zero,</span></div>
<div class="line"><a name="l00516"></a><span class="lineno">  516</span>&#160;<span class="comment">     *  exponentially scaled</span></div>
<div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00518"></a><span class="lineno">  518</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00520"></a><span class="lineno">  520</span>&#160;<span class="comment">     * SYNOPSIS:</span></div>
<div class="line"><a name="l00521"></a><span class="lineno">  521</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00522"></a><span class="lineno">  522</span>&#160;<span class="comment">     * double x, y, k0e();</span></div>
<div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00524"></a><span class="lineno">  524</span>&#160;<span class="comment">     * y = k0e( x );</span></div>
<div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160;<span class="comment">     * DESCRIPTION:</span></div>
<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160;<span class="comment">     * Returns exponentially scaled modified Bessel function</span></div>
<div class="line"><a name="l00531"></a><span class="lineno">  531</span>&#160;<span class="comment">     * of the third kind of order zero of the argument.</span></div>
<div class="line"><a name="l00532"></a><span class="lineno">  532</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00533"></a><span class="lineno">  533</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00534"></a><span class="lineno">  534</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00535"></a><span class="lineno">  535</span>&#160;<span class="comment">     * ACCURACY:</span></div>
<div class="line"><a name="l00536"></a><span class="lineno">  536</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00537"></a><span class="lineno">  537</span>&#160;<span class="comment">     *                      Relative error:</span></div>
<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;<span class="comment">     * arithmetic   domain     # trials      peak         rms</span></div>
<div class="line"><a name="l00539"></a><span class="lineno">  539</span>&#160;<span class="comment">     *    IEEE      0, 30       30000       1.4e-15     1.4e-16</span></div>
<div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160;<span class="comment">     * See k0().</span></div>
<div class="line"><a name="l00541"></a><span class="lineno">  541</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00542"></a><span class="lineno">  542</span>&#160;<span class="comment">     */</span></div>
<div class="line"><a name="l00543"></a><span class="lineno">  543</span>&#160; </div>
<div class="line"><a name="l00544"></a><span class="lineno">  544</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> A[] = {</div>
<div class="line"><a name="l00545"></a><span class="lineno">  545</span>&#160;      1.37446543561352307156E-16,</div>
<div class="line"><a name="l00546"></a><span class="lineno">  546</span>&#160;      4.25981614279661018399E-14,</div>
<div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160;      1.03496952576338420167E-11,</div>
<div class="line"><a name="l00548"></a><span class="lineno">  548</span>&#160;      1.90451637722020886025E-9,</div>
<div class="line"><a name="l00549"></a><span class="lineno">  549</span>&#160;      2.53479107902614945675E-7,</div>
<div class="line"><a name="l00550"></a><span class="lineno">  550</span>&#160;      2.28621210311945178607E-5,</div>
<div class="line"><a name="l00551"></a><span class="lineno">  551</span>&#160;      1.26461541144692592338E-3,</div>
<div class="line"><a name="l00552"></a><span class="lineno">  552</span>&#160;      3.59799365153615016266E-2,</div>
<div class="line"><a name="l00553"></a><span class="lineno">  553</span>&#160;      3.44289899924628486886E-1,</div>
<div class="line"><a name="l00554"></a><span class="lineno">  554</span>&#160;      -5.35327393233902768720E-1};</div>
<div class="line"><a name="l00555"></a><span class="lineno">  555</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> B[] = {</div>
<div class="line"><a name="l00556"></a><span class="lineno">  556</span>&#160;       5.30043377268626276149E-18, -1.64758043015242134646E-17,</div>
<div class="line"><a name="l00557"></a><span class="lineno">  557</span>&#160;       5.21039150503902756861E-17, -1.67823109680541210385E-16,</div>
<div class="line"><a name="l00558"></a><span class="lineno">  558</span>&#160;       5.51205597852431940784E-16, -1.84859337734377901440E-15,</div>
<div class="line"><a name="l00559"></a><span class="lineno">  559</span>&#160;       6.34007647740507060557E-15, -2.22751332699166985548E-14,</div>
<div class="line"><a name="l00560"></a><span class="lineno">  560</span>&#160;       8.03289077536357521100E-14, -2.98009692317273043925E-13,</div>
<div class="line"><a name="l00561"></a><span class="lineno">  561</span>&#160;       1.14034058820847496303E-12, -4.51459788337394416547E-12,</div>
<div class="line"><a name="l00562"></a><span class="lineno">  562</span>&#160;       1.85594911495471785253E-11, -7.95748924447710747776E-11,</div>
<div class="line"><a name="l00563"></a><span class="lineno">  563</span>&#160;       3.57739728140030116597E-10, -1.69753450938905987466E-9,</div>
<div class="line"><a name="l00564"></a><span class="lineno">  564</span>&#160;       8.57403401741422608519E-9, -4.66048989768794782956E-8,</div>
<div class="line"><a name="l00565"></a><span class="lineno">  565</span>&#160;       2.76681363944501510342E-7, -1.83175552271911948767E-6,</div>
<div class="line"><a name="l00566"></a><span class="lineno">  566</span>&#160;       1.39498137188764993662E-5, -1.28495495816278026384E-4,</div>
<div class="line"><a name="l00567"></a><span class="lineno">  567</span>&#160;       1.56988388573005337491E-3, -3.14481013119645005427E-2,</div>
<div class="line"><a name="l00568"></a><span class="lineno">  568</span>&#160;       2.44030308206595545468E0</div>
<div class="line"><a name="l00569"></a><span class="lineno">  569</span>&#160;    };</div>
<div class="line"><a name="l00570"></a><span class="lineno">  570</span>&#160;    <span class="keyword">const</span> T MAXNUM = pset1&lt;T&gt;(NumTraits&lt;double&gt;::infinity());</div>
<div class="line"><a name="l00571"></a><span class="lineno">  571</span>&#160;    <span class="keyword">const</span> T two = pset1&lt;T&gt;(2.0);</div>
<div class="line"><a name="l00572"></a><span class="lineno">  572</span>&#160;    T x_le_two = internal::pchebevl&lt;T, 10&gt;::run(</div>
<div class="line"><a name="l00573"></a><span class="lineno">  573</span>&#160;        pmadd(x, x, pset1&lt;T&gt;(-2.0)), A);</div>
<div class="line"><a name="l00574"></a><span class="lineno">  574</span>&#160;    x_le_two = pmadd(</div>
<div class="line"><a name="l00575"></a><span class="lineno">  575</span>&#160;        generic_i0&lt;T, double&gt;::run(x), pmul(</div>
<div class="line"><a name="l00576"></a><span class="lineno">  576</span>&#160;            pset1&lt;T&gt;(-1.0), plog(pmul(pset1&lt;T&gt;(0.5), x))), x_le_two);</div>
<div class="line"><a name="l00577"></a><span class="lineno">  577</span>&#160;    x_le_two = pmul(pexp(x), x_le_two);</div>
<div class="line"><a name="l00578"></a><span class="lineno">  578</span>&#160;    x_le_two = pselect(pcmp_le(x, pset1&lt;T&gt;(0.0)), MAXNUM, x_le_two);</div>
<div class="line"><a name="l00579"></a><span class="lineno">  579</span>&#160;    T x_gt_two = pmul(</div>
<div class="line"><a name="l00580"></a><span class="lineno">  580</span>&#160;            internal::pchebevl&lt;T, 25&gt;::run(</div>
<div class="line"><a name="l00581"></a><span class="lineno">  581</span>&#160;                psub(pdiv(pset1&lt;T&gt;(8.0), x), two), B),</div>
<div class="line"><a name="l00582"></a><span class="lineno">  582</span>&#160;            prsqrt(x));</div>
<div class="line"><a name="l00583"></a><span class="lineno">  583</span>&#160;    <span class="keywordflow">return</span> pselect(pcmp_le(x, two), x_le_two, x_gt_two);</div>
<div class="line"><a name="l00584"></a><span class="lineno">  584</span>&#160;  }</div>
<div class="line"><a name="l00585"></a><span class="lineno">  585</span>&#160;};</div>
<div class="line"><a name="l00586"></a><span class="lineno">  586</span>&#160; </div>
<div class="line"><a name="l00587"></a><span class="lineno">  587</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00588"></a><span class="lineno">  588</span>&#160;<span class="keyword">struct </span>bessel_k0e_impl {</div>
<div class="line"><a name="l00589"></a><span class="lineno">  589</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00590"></a><span class="lineno">  590</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T x) {</div>
<div class="line"><a name="l00591"></a><span class="lineno">  591</span>&#160;    <span class="keywordflow">return</span> generic_k0e&lt;T&gt;::run(x);</div>
<div class="line"><a name="l00592"></a><span class="lineno">  592</span>&#160;  }</div>
<div class="line"><a name="l00593"></a><span class="lineno">  593</span>&#160;};</div>
<div class="line"><a name="l00594"></a><span class="lineno">  594</span>&#160; </div>
<div class="line"><a name="l00595"></a><span class="lineno">  595</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00596"></a><span class="lineno">  596</span>&#160;<span class="keyword">struct </span>bessel_k0_retval {</div>
<div class="line"><a name="l00597"></a><span class="lineno">  597</span>&#160;  <span class="keyword">typedef</span> T type;</div>
<div class="line"><a name="l00598"></a><span class="lineno">  598</span>&#160;};</div>
<div class="line"><a name="l00599"></a><span class="lineno">  599</span>&#160; </div>
<div class="line"><a name="l00600"></a><span class="lineno">  600</span>&#160;template &lt;typename T, typename ScalarType = typename unpacket_traits&lt;T&gt;::type&gt;</div>
<div class="line"><a name="l00601"></a><span class="lineno">  601</span>&#160;<span class="keyword">struct </span>generic_k0 {</div>
<div class="line"><a name="l00602"></a><span class="lineno">  602</span>&#160;  EIGEN_STATIC_ASSERT((internal::is_same&lt;T, T&gt;::value == <span class="keyword">false</span>),</div>
<div class="line"><a name="l00603"></a><span class="lineno">  603</span>&#160;                      THIS_TYPE_IS_NOT_SUPPORTED)</div>
<div class="line"><a name="l00604"></a><span class="lineno">  604</span>&#160; </div>
<div class="line"><a name="l00605"></a><span class="lineno">  605</span>&#160;  EIGEN_DEVICE_FUNC <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp;) {</div>
<div class="line"><a name="l00606"></a><span class="lineno">  606</span>&#160;    <span class="keywordflow">return</span> ScalarType(0);</div>
<div class="line"><a name="l00607"></a><span class="lineno">  607</span>&#160;  }</div>
<div class="line"><a name="l00608"></a><span class="lineno">  608</span>&#160;};</div>
<div class="line"><a name="l00609"></a><span class="lineno">  609</span>&#160; </div>
<div class="line"><a name="l00610"></a><span class="lineno">  610</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00611"></a><span class="lineno">  611</span>&#160;<span class="keyword">struct </span>generic_k0&lt;T, float&gt; {</div>
<div class="line"><a name="l00612"></a><span class="lineno">  612</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00613"></a><span class="lineno">  613</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp; x) {</div>
<div class="line"><a name="l00614"></a><span class="lineno">  614</span>&#160;    <span class="comment">/*  k0f.c</span></div>
<div class="line"><a name="l00615"></a><span class="lineno">  615</span>&#160;<span class="comment">     *  Modified Bessel function, third kind, order zero</span></div>
<div class="line"><a name="l00616"></a><span class="lineno">  616</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00617"></a><span class="lineno">  617</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00618"></a><span class="lineno">  618</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00619"></a><span class="lineno">  619</span>&#160;<span class="comment">     * SYNOPSIS:</span></div>
<div class="line"><a name="l00620"></a><span class="lineno">  620</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00621"></a><span class="lineno">  621</span>&#160;<span class="comment">     * float x, y, k0f();</span></div>
<div class="line"><a name="l00622"></a><span class="lineno">  622</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00623"></a><span class="lineno">  623</span>&#160;<span class="comment">     * y = k0f( x );</span></div>
<div class="line"><a name="l00624"></a><span class="lineno">  624</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00625"></a><span class="lineno">  625</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00626"></a><span class="lineno">  626</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00627"></a><span class="lineno">  627</span>&#160;<span class="comment">     * DESCRIPTION:</span></div>
<div class="line"><a name="l00628"></a><span class="lineno">  628</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00629"></a><span class="lineno">  629</span>&#160;<span class="comment">     * Returns modified Bessel function of the third kind</span></div>
<div class="line"><a name="l00630"></a><span class="lineno">  630</span>&#160;<span class="comment">     * of order zero of the argument.</span></div>
<div class="line"><a name="l00631"></a><span class="lineno">  631</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00632"></a><span class="lineno">  632</span>&#160;<span class="comment">     * The range is partitioned into the two intervals [0,8] and</span></div>
<div class="line"><a name="l00633"></a><span class="lineno">  633</span>&#160;<span class="comment">     * (8, infinity).  Chebyshev polynomial expansions are employed</span></div>
<div class="line"><a name="l00634"></a><span class="lineno">  634</span>&#160;<span class="comment">     * in each interval.</span></div>
<div class="line"><a name="l00635"></a><span class="lineno">  635</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00636"></a><span class="lineno">  636</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00637"></a><span class="lineno">  637</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00638"></a><span class="lineno">  638</span>&#160;<span class="comment">     * ACCURACY:</span></div>
<div class="line"><a name="l00639"></a><span class="lineno">  639</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00640"></a><span class="lineno">  640</span>&#160;<span class="comment">     * Tested at 2000 random points between 0 and 8.  Peak absolute</span></div>
<div class="line"><a name="l00641"></a><span class="lineno">  641</span>&#160;<span class="comment">     * error (relative when K0 &gt; 1) was 1.46e-14; rms, 4.26e-15.</span></div>
<div class="line"><a name="l00642"></a><span class="lineno">  642</span>&#160;<span class="comment">     *                      Relative error:</span></div>
<div class="line"><a name="l00643"></a><span class="lineno">  643</span>&#160;<span class="comment">     * arithmetic   domain     # trials      peak         rms</span></div>
<div class="line"><a name="l00644"></a><span class="lineno">  644</span>&#160;<span class="comment">     *    IEEE      0, 30       30000       7.8e-7      8.5e-8</span></div>
<div class="line"><a name="l00645"></a><span class="lineno">  645</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00646"></a><span class="lineno">  646</span>&#160;<span class="comment">     * ERROR MESSAGES:</span></div>
<div class="line"><a name="l00647"></a><span class="lineno">  647</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00648"></a><span class="lineno">  648</span>&#160;<span class="comment">     *   message         condition      value returned</span></div>
<div class="line"><a name="l00649"></a><span class="lineno">  649</span>&#160;<span class="comment">     *  K0 domain          x &lt;= 0          MAXNUM</span></div>
<div class="line"><a name="l00650"></a><span class="lineno">  650</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00651"></a><span class="lineno">  651</span>&#160;<span class="comment">     */</span></div>
<div class="line"><a name="l00652"></a><span class="lineno">  652</span>&#160; </div>
<div class="line"><a name="l00653"></a><span class="lineno">  653</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> A[] = {1.90451637722020886025E-9f, 2.53479107902614945675E-7f,</div>
<div class="line"><a name="l00654"></a><span class="lineno">  654</span>&#160;                       2.28621210311945178607E-5f, 1.26461541144692592338E-3f,</div>
<div class="line"><a name="l00655"></a><span class="lineno">  655</span>&#160;                       3.59799365153615016266E-2f, 3.44289899924628486886E-1f,</div>
<div class="line"><a name="l00656"></a><span class="lineno">  656</span>&#160;                       -5.35327393233902768720E-1f};</div>
<div class="line"><a name="l00657"></a><span class="lineno">  657</span>&#160; </div>
<div class="line"><a name="l00658"></a><span class="lineno">  658</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> B[] = {-1.69753450938905987466E-9f, 8.57403401741422608519E-9f,</div>
<div class="line"><a name="l00659"></a><span class="lineno">  659</span>&#160;                       -4.66048989768794782956E-8f, 2.76681363944501510342E-7f,</div>
<div class="line"><a name="l00660"></a><span class="lineno">  660</span>&#160;                       -1.83175552271911948767E-6f, 1.39498137188764993662E-5f,</div>
<div class="line"><a name="l00661"></a><span class="lineno">  661</span>&#160;                       -1.28495495816278026384E-4f, 1.56988388573005337491E-3f,</div>
<div class="line"><a name="l00662"></a><span class="lineno">  662</span>&#160;                       -3.14481013119645005427E-2f, 2.44030308206595545468E0f};</div>
<div class="line"><a name="l00663"></a><span class="lineno">  663</span>&#160;    <span class="keyword">const</span> T MAXNUM = pset1&lt;T&gt;(NumTraits&lt;float&gt;::infinity());</div>
<div class="line"><a name="l00664"></a><span class="lineno">  664</span>&#160;    <span class="keyword">const</span> T two = pset1&lt;T&gt;(2.0);</div>
<div class="line"><a name="l00665"></a><span class="lineno">  665</span>&#160;    T x_le_two = internal::pchebevl&lt;T, 7&gt;::run(</div>
<div class="line"><a name="l00666"></a><span class="lineno">  666</span>&#160;        pmadd(x, x, pset1&lt;T&gt;(-2.0)), A);</div>
<div class="line"><a name="l00667"></a><span class="lineno">  667</span>&#160;    x_le_two = pmadd(</div>
<div class="line"><a name="l00668"></a><span class="lineno">  668</span>&#160;        generic_i0&lt;T, float&gt;::run(x), pnegate(</div>
<div class="line"><a name="l00669"></a><span class="lineno">  669</span>&#160;            plog(pmul(pset1&lt;T&gt;(0.5), x))), x_le_two);</div>
<div class="line"><a name="l00670"></a><span class="lineno">  670</span>&#160;    x_le_two = pselect(pcmp_le(x, pset1&lt;T&gt;(0.0)), MAXNUM, x_le_two);</div>
<div class="line"><a name="l00671"></a><span class="lineno">  671</span>&#160;    T x_gt_two = pmul(</div>
<div class="line"><a name="l00672"></a><span class="lineno">  672</span>&#160;        pmul(</div>
<div class="line"><a name="l00673"></a><span class="lineno">  673</span>&#160;            pexp(pnegate(x)),</div>
<div class="line"><a name="l00674"></a><span class="lineno">  674</span>&#160;            internal::pchebevl&lt;T, 10&gt;::run(</div>
<div class="line"><a name="l00675"></a><span class="lineno">  675</span>&#160;                psub(pdiv(pset1&lt;T&gt;(8.0), x), two), B)),</div>
<div class="line"><a name="l00676"></a><span class="lineno">  676</span>&#160;        prsqrt(x));</div>
<div class="line"><a name="l00677"></a><span class="lineno">  677</span>&#160;    <span class="keywordflow">return</span> pselect(pcmp_le(x, two), x_le_two, x_gt_two);</div>
<div class="line"><a name="l00678"></a><span class="lineno">  678</span>&#160;  }</div>
<div class="line"><a name="l00679"></a><span class="lineno">  679</span>&#160;};</div>
<div class="line"><a name="l00680"></a><span class="lineno">  680</span>&#160; </div>
<div class="line"><a name="l00681"></a><span class="lineno">  681</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00682"></a><span class="lineno">  682</span>&#160;<span class="keyword">struct </span>generic_k0&lt;T, double&gt; {</div>
<div class="line"><a name="l00683"></a><span class="lineno">  683</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00684"></a><span class="lineno">  684</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp; x) {</div>
<div class="line"><a name="l00685"></a><span class="lineno">  685</span>&#160;    <span class="comment">/*</span></div>
<div class="line"><a name="l00686"></a><span class="lineno">  686</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00687"></a><span class="lineno">  687</span>&#160;<span class="comment">     *  Modified Bessel function, third kind, order zero,</span></div>
<div class="line"><a name="l00688"></a><span class="lineno">  688</span>&#160;<span class="comment">     *  exponentially scaled</span></div>
<div class="line"><a name="l00689"></a><span class="lineno">  689</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00690"></a><span class="lineno">  690</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00691"></a><span class="lineno">  691</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00692"></a><span class="lineno">  692</span>&#160;<span class="comment">     * SYNOPSIS:</span></div>
<div class="line"><a name="l00693"></a><span class="lineno">  693</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00694"></a><span class="lineno">  694</span>&#160;<span class="comment">     * double x, y, k0();</span></div>
<div class="line"><a name="l00695"></a><span class="lineno">  695</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00696"></a><span class="lineno">  696</span>&#160;<span class="comment">     * y = k0( x );</span></div>
<div class="line"><a name="l00697"></a><span class="lineno">  697</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00698"></a><span class="lineno">  698</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00699"></a><span class="lineno">  699</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00700"></a><span class="lineno">  700</span>&#160;<span class="comment">     * DESCRIPTION:</span></div>
<div class="line"><a name="l00701"></a><span class="lineno">  701</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00702"></a><span class="lineno">  702</span>&#160;<span class="comment">     * Returns exponentially scaled modified Bessel function</span></div>
<div class="line"><a name="l00703"></a><span class="lineno">  703</span>&#160;<span class="comment">     * of the third kind of order zero of the argument.</span></div>
<div class="line"><a name="l00704"></a><span class="lineno">  704</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00705"></a><span class="lineno">  705</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00706"></a><span class="lineno">  706</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00707"></a><span class="lineno">  707</span>&#160;<span class="comment">     * ACCURACY:</span></div>
<div class="line"><a name="l00708"></a><span class="lineno">  708</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00709"></a><span class="lineno">  709</span>&#160;<span class="comment">     *                      Relative error:</span></div>
<div class="line"><a name="l00710"></a><span class="lineno">  710</span>&#160;<span class="comment">     * arithmetic   domain     # trials      peak         rms</span></div>
<div class="line"><a name="l00711"></a><span class="lineno">  711</span>&#160;<span class="comment">     *    IEEE      0, 30       30000       1.4e-15     1.4e-16</span></div>
<div class="line"><a name="l00712"></a><span class="lineno">  712</span>&#160;<span class="comment">     * See k0().</span></div>
<div class="line"><a name="l00713"></a><span class="lineno">  713</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00714"></a><span class="lineno">  714</span>&#160;<span class="comment">     */</span></div>
<div class="line"><a name="l00715"></a><span class="lineno">  715</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> A[] = {</div>
<div class="line"><a name="l00716"></a><span class="lineno">  716</span>&#160;      1.37446543561352307156E-16,</div>
<div class="line"><a name="l00717"></a><span class="lineno">  717</span>&#160;      4.25981614279661018399E-14,</div>
<div class="line"><a name="l00718"></a><span class="lineno">  718</span>&#160;      1.03496952576338420167E-11,</div>
<div class="line"><a name="l00719"></a><span class="lineno">  719</span>&#160;      1.90451637722020886025E-9,</div>
<div class="line"><a name="l00720"></a><span class="lineno">  720</span>&#160;      2.53479107902614945675E-7,</div>
<div class="line"><a name="l00721"></a><span class="lineno">  721</span>&#160;      2.28621210311945178607E-5,</div>
<div class="line"><a name="l00722"></a><span class="lineno">  722</span>&#160;      1.26461541144692592338E-3,</div>
<div class="line"><a name="l00723"></a><span class="lineno">  723</span>&#160;      3.59799365153615016266E-2,</div>
<div class="line"><a name="l00724"></a><span class="lineno">  724</span>&#160;      3.44289899924628486886E-1,</div>
<div class="line"><a name="l00725"></a><span class="lineno">  725</span>&#160;      -5.35327393233902768720E-1};</div>
<div class="line"><a name="l00726"></a><span class="lineno">  726</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> B[] = {</div>
<div class="line"><a name="l00727"></a><span class="lineno">  727</span>&#160;       5.30043377268626276149E-18, -1.64758043015242134646E-17,</div>
<div class="line"><a name="l00728"></a><span class="lineno">  728</span>&#160;       5.21039150503902756861E-17, -1.67823109680541210385E-16,</div>
<div class="line"><a name="l00729"></a><span class="lineno">  729</span>&#160;       5.51205597852431940784E-16, -1.84859337734377901440E-15,</div>
<div class="line"><a name="l00730"></a><span class="lineno">  730</span>&#160;       6.34007647740507060557E-15, -2.22751332699166985548E-14,</div>
<div class="line"><a name="l00731"></a><span class="lineno">  731</span>&#160;       8.03289077536357521100E-14, -2.98009692317273043925E-13,</div>
<div class="line"><a name="l00732"></a><span class="lineno">  732</span>&#160;       1.14034058820847496303E-12, -4.51459788337394416547E-12,</div>
<div class="line"><a name="l00733"></a><span class="lineno">  733</span>&#160;       1.85594911495471785253E-11, -7.95748924447710747776E-11,</div>
<div class="line"><a name="l00734"></a><span class="lineno">  734</span>&#160;       3.57739728140030116597E-10, -1.69753450938905987466E-9,</div>
<div class="line"><a name="l00735"></a><span class="lineno">  735</span>&#160;       8.57403401741422608519E-9, -4.66048989768794782956E-8,</div>
<div class="line"><a name="l00736"></a><span class="lineno">  736</span>&#160;       2.76681363944501510342E-7, -1.83175552271911948767E-6,</div>
<div class="line"><a name="l00737"></a><span class="lineno">  737</span>&#160;       1.39498137188764993662E-5, -1.28495495816278026384E-4,</div>
<div class="line"><a name="l00738"></a><span class="lineno">  738</span>&#160;       1.56988388573005337491E-3, -3.14481013119645005427E-2,</div>
<div class="line"><a name="l00739"></a><span class="lineno">  739</span>&#160;       2.44030308206595545468E0</div>
<div class="line"><a name="l00740"></a><span class="lineno">  740</span>&#160;    };</div>
<div class="line"><a name="l00741"></a><span class="lineno">  741</span>&#160;    <span class="keyword">const</span> T MAXNUM = pset1&lt;T&gt;(NumTraits&lt;double&gt;::infinity());</div>
<div class="line"><a name="l00742"></a><span class="lineno">  742</span>&#160;    <span class="keyword">const</span> T two = pset1&lt;T&gt;(2.0);</div>
<div class="line"><a name="l00743"></a><span class="lineno">  743</span>&#160;    T x_le_two = internal::pchebevl&lt;T, 10&gt;::run(</div>
<div class="line"><a name="l00744"></a><span class="lineno">  744</span>&#160;        pmadd(x, x, pset1&lt;T&gt;(-2.0)), A);</div>
<div class="line"><a name="l00745"></a><span class="lineno">  745</span>&#160;    x_le_two = pmadd(</div>
<div class="line"><a name="l00746"></a><span class="lineno">  746</span>&#160;        generic_i0&lt;T, double&gt;::run(x), pnegate(</div>
<div class="line"><a name="l00747"></a><span class="lineno">  747</span>&#160;            plog(pmul(pset1&lt;T&gt;(0.5), x))), x_le_two);</div>
<div class="line"><a name="l00748"></a><span class="lineno">  748</span>&#160;    x_le_two = pselect(pcmp_le(x, pset1&lt;T&gt;(0.0)), MAXNUM, x_le_two);</div>
<div class="line"><a name="l00749"></a><span class="lineno">  749</span>&#160;    T x_gt_two = pmul(</div>
<div class="line"><a name="l00750"></a><span class="lineno">  750</span>&#160;        pmul(</div>
<div class="line"><a name="l00751"></a><span class="lineno">  751</span>&#160;            pexp(-x),</div>
<div class="line"><a name="l00752"></a><span class="lineno">  752</span>&#160;            internal::pchebevl&lt;T, 25&gt;::run(</div>
<div class="line"><a name="l00753"></a><span class="lineno">  753</span>&#160;                psub(pdiv(pset1&lt;T&gt;(8.0), x), two), B)),</div>
<div class="line"><a name="l00754"></a><span class="lineno">  754</span>&#160;        prsqrt(x));</div>
<div class="line"><a name="l00755"></a><span class="lineno">  755</span>&#160;    <span class="keywordflow">return</span> pselect(pcmp_le(x, two), x_le_two, x_gt_two);</div>
<div class="line"><a name="l00756"></a><span class="lineno">  756</span>&#160;  }</div>
<div class="line"><a name="l00757"></a><span class="lineno">  757</span>&#160;};</div>
<div class="line"><a name="l00758"></a><span class="lineno">  758</span>&#160; </div>
<div class="line"><a name="l00759"></a><span class="lineno">  759</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00760"></a><span class="lineno">  760</span>&#160;<span class="keyword">struct </span>bessel_k0_impl {</div>
<div class="line"><a name="l00761"></a><span class="lineno">  761</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00762"></a><span class="lineno">  762</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T x) {</div>
<div class="line"><a name="l00763"></a><span class="lineno">  763</span>&#160;    <span class="keywordflow">return</span> generic_k0&lt;T&gt;::run(x);</div>
<div class="line"><a name="l00764"></a><span class="lineno">  764</span>&#160;  }</div>
<div class="line"><a name="l00765"></a><span class="lineno">  765</span>&#160;};</div>
<div class="line"><a name="l00766"></a><span class="lineno">  766</span>&#160; </div>
<div class="line"><a name="l00767"></a><span class="lineno">  767</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00768"></a><span class="lineno">  768</span>&#160;<span class="keyword">struct </span>bessel_k1e_retval {</div>
<div class="line"><a name="l00769"></a><span class="lineno">  769</span>&#160;  <span class="keyword">typedef</span> T type;</div>
<div class="line"><a name="l00770"></a><span class="lineno">  770</span>&#160;};</div>
<div class="line"><a name="l00771"></a><span class="lineno">  771</span>&#160; </div>
<div class="line"><a name="l00772"></a><span class="lineno">  772</span>&#160;template &lt;typename T, typename ScalarType = typename unpacket_traits&lt;T&gt;::type&gt;</div>
<div class="line"><a name="l00773"></a><span class="lineno">  773</span>&#160;<span class="keyword">struct </span>generic_k1e {</div>
<div class="line"><a name="l00774"></a><span class="lineno">  774</span>&#160;  EIGEN_STATIC_ASSERT((internal::is_same&lt;T, T&gt;::value == <span class="keyword">false</span>),</div>
<div class="line"><a name="l00775"></a><span class="lineno">  775</span>&#160;                      THIS_TYPE_IS_NOT_SUPPORTED)</div>
<div class="line"><a name="l00776"></a><span class="lineno">  776</span>&#160; </div>
<div class="line"><a name="l00777"></a><span class="lineno">  777</span>&#160;  EIGEN_DEVICE_FUNC <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp;) {</div>
<div class="line"><a name="l00778"></a><span class="lineno">  778</span>&#160;    <span class="keywordflow">return</span> ScalarType(0);</div>
<div class="line"><a name="l00779"></a><span class="lineno">  779</span>&#160;  }</div>
<div class="line"><a name="l00780"></a><span class="lineno">  780</span>&#160;};</div>
<div class="line"><a name="l00781"></a><span class="lineno">  781</span>&#160; </div>
<div class="line"><a name="l00782"></a><span class="lineno">  782</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00783"></a><span class="lineno">  783</span>&#160;<span class="keyword">struct </span>generic_k1e&lt;T, float&gt; {</div>
<div class="line"><a name="l00784"></a><span class="lineno">  784</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00785"></a><span class="lineno">  785</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp; x) {</div>
<div class="line"><a name="l00786"></a><span class="lineno">  786</span>&#160;    <span class="comment">/* k1ef.c</span></div>
<div class="line"><a name="l00787"></a><span class="lineno">  787</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00788"></a><span class="lineno">  788</span>&#160;<span class="comment">     *  Modified Bessel function, third kind, order one,</span></div>
<div class="line"><a name="l00789"></a><span class="lineno">  789</span>&#160;<span class="comment">     *  exponentially scaled</span></div>
<div class="line"><a name="l00790"></a><span class="lineno">  790</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00791"></a><span class="lineno">  791</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00792"></a><span class="lineno">  792</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00793"></a><span class="lineno">  793</span>&#160;<span class="comment">     * SYNOPSIS:</span></div>
<div class="line"><a name="l00794"></a><span class="lineno">  794</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00795"></a><span class="lineno">  795</span>&#160;<span class="comment">     * float x, y, k1ef();</span></div>
<div class="line"><a name="l00796"></a><span class="lineno">  796</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00797"></a><span class="lineno">  797</span>&#160;<span class="comment">     * y = k1ef( x );</span></div>
<div class="line"><a name="l00798"></a><span class="lineno">  798</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00799"></a><span class="lineno">  799</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00800"></a><span class="lineno">  800</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00801"></a><span class="lineno">  801</span>&#160;<span class="comment">     * DESCRIPTION:</span></div>
<div class="line"><a name="l00802"></a><span class="lineno">  802</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00803"></a><span class="lineno">  803</span>&#160;<span class="comment">     * Returns exponentially scaled modified Bessel function</span></div>
<div class="line"><a name="l00804"></a><span class="lineno">  804</span>&#160;<span class="comment">     * of the third kind of order one of the argument:</span></div>
<div class="line"><a name="l00805"></a><span class="lineno">  805</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00806"></a><span class="lineno">  806</span>&#160;<span class="comment">     *      k1e(x) = exp(x) * k1(x).</span></div>
<div class="line"><a name="l00807"></a><span class="lineno">  807</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00808"></a><span class="lineno">  808</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00809"></a><span class="lineno">  809</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00810"></a><span class="lineno">  810</span>&#160;<span class="comment">     * ACCURACY:</span></div>
<div class="line"><a name="l00811"></a><span class="lineno">  811</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00812"></a><span class="lineno">  812</span>&#160;<span class="comment">     *                      Relative error:</span></div>
<div class="line"><a name="l00813"></a><span class="lineno">  813</span>&#160;<span class="comment">     * arithmetic   domain     # trials      peak         rms</span></div>
<div class="line"><a name="l00814"></a><span class="lineno">  814</span>&#160;<span class="comment">     *    IEEE      0, 30       30000       4.9e-7      6.7e-8</span></div>
<div class="line"><a name="l00815"></a><span class="lineno">  815</span>&#160;<span class="comment">     * See k1().</span></div>
<div class="line"><a name="l00816"></a><span class="lineno">  816</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00817"></a><span class="lineno">  817</span>&#160;<span class="comment">     */</span></div>
<div class="line"><a name="l00818"></a><span class="lineno">  818</span>&#160; </div>
<div class="line"><a name="l00819"></a><span class="lineno">  819</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> A[] = {-2.21338763073472585583E-8f, -2.43340614156596823496E-6f,</div>
<div class="line"><a name="l00820"></a><span class="lineno">  820</span>&#160;                        -1.73028895751305206302E-4f, -6.97572385963986435018E-3f,</div>
<div class="line"><a name="l00821"></a><span class="lineno">  821</span>&#160;                        -1.22611180822657148235E-1f, -3.53155960776544875667E-1f,</div>
<div class="line"><a name="l00822"></a><span class="lineno">  822</span>&#160;                        1.52530022733894777053E0f};</div>
<div class="line"><a name="l00823"></a><span class="lineno">  823</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> B[] = {2.01504975519703286596E-9f, -1.03457624656780970260E-8f,</div>
<div class="line"><a name="l00824"></a><span class="lineno">  824</span>&#160;                       5.74108412545004946722E-8f, -3.50196060308781257119E-7f,</div>
<div class="line"><a name="l00825"></a><span class="lineno">  825</span>&#160;                       2.40648494783721712015E-6f, -1.93619797416608296024E-5f,</div>
<div class="line"><a name="l00826"></a><span class="lineno">  826</span>&#160;                       1.95215518471351631108E-4f, -2.85781685962277938680E-3f,</div>
<div class="line"><a name="l00827"></a><span class="lineno">  827</span>&#160;                       1.03923736576817238437E-1f, 2.72062619048444266945E0f};</div>
<div class="line"><a name="l00828"></a><span class="lineno">  828</span>&#160;    <span class="keyword">const</span> T MAXNUM = pset1&lt;T&gt;(NumTraits&lt;float&gt;::infinity());</div>
<div class="line"><a name="l00829"></a><span class="lineno">  829</span>&#160;    <span class="keyword">const</span> T two = pset1&lt;T&gt;(2.0);</div>
<div class="line"><a name="l00830"></a><span class="lineno">  830</span>&#160;    T x_le_two = pdiv(internal::pchebevl&lt;T, 7&gt;::run(</div>
<div class="line"><a name="l00831"></a><span class="lineno">  831</span>&#160;        pmadd(x, x, pset1&lt;T&gt;(-2.0)), A), x);</div>
<div class="line"><a name="l00832"></a><span class="lineno">  832</span>&#160;    x_le_two = pmadd(</div>
<div class="line"><a name="l00833"></a><span class="lineno">  833</span>&#160;        generic_i1&lt;T, float&gt;::run(x), plog(pmul(pset1&lt;T&gt;(0.5), x)), x_le_two);</div>
<div class="line"><a name="l00834"></a><span class="lineno">  834</span>&#160;    x_le_two = pmul(x_le_two, pexp(x));</div>
<div class="line"><a name="l00835"></a><span class="lineno">  835</span>&#160;    x_le_two = pselect(pcmp_le(x, pset1&lt;T&gt;(0.0)), MAXNUM, x_le_two);</div>
<div class="line"><a name="l00836"></a><span class="lineno">  836</span>&#160;    T x_gt_two = pmul(</div>
<div class="line"><a name="l00837"></a><span class="lineno">  837</span>&#160;        internal::pchebevl&lt;T, 10&gt;::run(</div>
<div class="line"><a name="l00838"></a><span class="lineno">  838</span>&#160;            psub(pdiv(pset1&lt;T&gt;(8.0), x), two), B),</div>
<div class="line"><a name="l00839"></a><span class="lineno">  839</span>&#160;        prsqrt(x));</div>
<div class="line"><a name="l00840"></a><span class="lineno">  840</span>&#160;    <span class="keywordflow">return</span> pselect(pcmp_le(x, two), x_le_two, x_gt_two);</div>
<div class="line"><a name="l00841"></a><span class="lineno">  841</span>&#160;  }</div>
<div class="line"><a name="l00842"></a><span class="lineno">  842</span>&#160;};</div>
<div class="line"><a name="l00843"></a><span class="lineno">  843</span>&#160; </div>
<div class="line"><a name="l00844"></a><span class="lineno">  844</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00845"></a><span class="lineno">  845</span>&#160;<span class="keyword">struct </span>generic_k1e&lt;T, double&gt; {</div>
<div class="line"><a name="l00846"></a><span class="lineno">  846</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00847"></a><span class="lineno">  847</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp; x) {</div>
<div class="line"><a name="l00848"></a><span class="lineno">  848</span>&#160;    <span class="comment">/*  k1e.c</span></div>
<div class="line"><a name="l00849"></a><span class="lineno">  849</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00850"></a><span class="lineno">  850</span>&#160;<span class="comment">     *  Modified Bessel function, third kind, order one,</span></div>
<div class="line"><a name="l00851"></a><span class="lineno">  851</span>&#160;<span class="comment">     *  exponentially scaled</span></div>
<div class="line"><a name="l00852"></a><span class="lineno">  852</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00853"></a><span class="lineno">  853</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00854"></a><span class="lineno">  854</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00855"></a><span class="lineno">  855</span>&#160;<span class="comment">     * SYNOPSIS:</span></div>
<div class="line"><a name="l00856"></a><span class="lineno">  856</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00857"></a><span class="lineno">  857</span>&#160;<span class="comment">     * double x, y, k1e();</span></div>
<div class="line"><a name="l00858"></a><span class="lineno">  858</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00859"></a><span class="lineno">  859</span>&#160;<span class="comment">     * y = k1e( x );</span></div>
<div class="line"><a name="l00860"></a><span class="lineno">  860</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00861"></a><span class="lineno">  861</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00862"></a><span class="lineno">  862</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00863"></a><span class="lineno">  863</span>&#160;<span class="comment">     * DESCRIPTION:</span></div>
<div class="line"><a name="l00864"></a><span class="lineno">  864</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00865"></a><span class="lineno">  865</span>&#160;<span class="comment">     * Returns exponentially scaled modified Bessel function</span></div>
<div class="line"><a name="l00866"></a><span class="lineno">  866</span>&#160;<span class="comment">     * of the third kind of order one of the argument:</span></div>
<div class="line"><a name="l00867"></a><span class="lineno">  867</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00868"></a><span class="lineno">  868</span>&#160;<span class="comment">     *      k1e(x) = exp(x) * k1(x).</span></div>
<div class="line"><a name="l00869"></a><span class="lineno">  869</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00870"></a><span class="lineno">  870</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00871"></a><span class="lineno">  871</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00872"></a><span class="lineno">  872</span>&#160;<span class="comment">     * ACCURACY:</span></div>
<div class="line"><a name="l00873"></a><span class="lineno">  873</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00874"></a><span class="lineno">  874</span>&#160;<span class="comment">     *                      Relative error:</span></div>
<div class="line"><a name="l00875"></a><span class="lineno">  875</span>&#160;<span class="comment">     * arithmetic   domain     # trials      peak         rms</span></div>
<div class="line"><a name="l00876"></a><span class="lineno">  876</span>&#160;<span class="comment">     *    IEEE      0, 30       30000       7.8e-16     1.2e-16</span></div>
<div class="line"><a name="l00877"></a><span class="lineno">  877</span>&#160;<span class="comment">     * See k1().</span></div>
<div class="line"><a name="l00878"></a><span class="lineno">  878</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00879"></a><span class="lineno">  879</span>&#160;<span class="comment">     */</span></div>
<div class="line"><a name="l00880"></a><span class="lineno">  880</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> A[] = {-7.02386347938628759343E-18, -2.42744985051936593393E-15,</div>
<div class="line"><a name="l00881"></a><span class="lineno">  881</span>&#160;                        -6.66690169419932900609E-13, -1.41148839263352776110E-10,</div>
<div class="line"><a name="l00882"></a><span class="lineno">  882</span>&#160;                        -2.21338763073472585583E-8, -2.43340614156596823496E-6,</div>
<div class="line"><a name="l00883"></a><span class="lineno">  883</span>&#160;                        -1.73028895751305206302E-4, -6.97572385963986435018E-3,</div>
<div class="line"><a name="l00884"></a><span class="lineno">  884</span>&#160;                        -1.22611180822657148235E-1, -3.53155960776544875667E-1,</div>
<div class="line"><a name="l00885"></a><span class="lineno">  885</span>&#160;                        1.52530022733894777053E0};</div>
<div class="line"><a name="l00886"></a><span class="lineno">  886</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> B[] = {-5.75674448366501715755E-18, 1.79405087314755922667E-17,</div>
<div class="line"><a name="l00887"></a><span class="lineno">  887</span>&#160;                        -5.68946255844285935196E-17, 1.83809354436663880070E-16,</div>
<div class="line"><a name="l00888"></a><span class="lineno">  888</span>&#160;                        -6.05704724837331885336E-16, 2.03870316562433424052E-15,</div>
<div class="line"><a name="l00889"></a><span class="lineno">  889</span>&#160;                        -7.01983709041831346144E-15, 2.47715442448130437068E-14,</div>
<div class="line"><a name="l00890"></a><span class="lineno">  890</span>&#160;                        -8.97670518232499435011E-14, 3.34841966607842919884E-13,</div>
<div class="line"><a name="l00891"></a><span class="lineno">  891</span>&#160;                        -1.28917396095102890680E-12, 5.13963967348173025100E-12,</div>
<div class="line"><a name="l00892"></a><span class="lineno">  892</span>&#160;                        -2.12996783842756842877E-11, 9.21831518760500529508E-11,</div>
<div class="line"><a name="l00893"></a><span class="lineno">  893</span>&#160;                        -4.19035475934189648750E-10, 2.01504975519703286596E-9,</div>
<div class="line"><a name="l00894"></a><span class="lineno">  894</span>&#160;                        -1.03457624656780970260E-8, 5.74108412545004946722E-8,</div>
<div class="line"><a name="l00895"></a><span class="lineno">  895</span>&#160;                        -3.50196060308781257119E-7, 2.40648494783721712015E-6,</div>
<div class="line"><a name="l00896"></a><span class="lineno">  896</span>&#160;                        -1.93619797416608296024E-5, 1.95215518471351631108E-4,</div>
<div class="line"><a name="l00897"></a><span class="lineno">  897</span>&#160;                        -2.85781685962277938680E-3, 1.03923736576817238437E-1,</div>
<div class="line"><a name="l00898"></a><span class="lineno">  898</span>&#160;                        2.72062619048444266945E0};</div>
<div class="line"><a name="l00899"></a><span class="lineno">  899</span>&#160;    <span class="keyword">const</span> T MAXNUM = pset1&lt;T&gt;(NumTraits&lt;double&gt;::infinity());</div>
<div class="line"><a name="l00900"></a><span class="lineno">  900</span>&#160;    <span class="keyword">const</span> T two = pset1&lt;T&gt;(2.0);</div>
<div class="line"><a name="l00901"></a><span class="lineno">  901</span>&#160;    T x_le_two = pdiv(internal::pchebevl&lt;T, 11&gt;::run(</div>
<div class="line"><a name="l00902"></a><span class="lineno">  902</span>&#160;        pmadd(x, x, pset1&lt;T&gt;(-2.0)), A), x);</div>
<div class="line"><a name="l00903"></a><span class="lineno">  903</span>&#160;    x_le_two = pmadd(</div>
<div class="line"><a name="l00904"></a><span class="lineno">  904</span>&#160;        generic_i1&lt;T, double&gt;::run(x), plog(pmul(pset1&lt;T&gt;(0.5), x)), x_le_two);</div>
<div class="line"><a name="l00905"></a><span class="lineno">  905</span>&#160;    x_le_two = pmul(x_le_two, pexp(x));</div>
<div class="line"><a name="l00906"></a><span class="lineno">  906</span>&#160;    x_le_two = pselect(pcmp_le(x, pset1&lt;T&gt;(0.0)), MAXNUM, x_le_two);</div>
<div class="line"><a name="l00907"></a><span class="lineno">  907</span>&#160;    T x_gt_two = pmul(</div>
<div class="line"><a name="l00908"></a><span class="lineno">  908</span>&#160;        internal::pchebevl&lt;T, 25&gt;::run(</div>
<div class="line"><a name="l00909"></a><span class="lineno">  909</span>&#160;            psub(pdiv(pset1&lt;T&gt;(8.0), x), two), B),</div>
<div class="line"><a name="l00910"></a><span class="lineno">  910</span>&#160;        prsqrt(x));</div>
<div class="line"><a name="l00911"></a><span class="lineno">  911</span>&#160;    <span class="keywordflow">return</span> pselect(pcmp_le(x, two), x_le_two, x_gt_two);</div>
<div class="line"><a name="l00912"></a><span class="lineno">  912</span>&#160;  }</div>
<div class="line"><a name="l00913"></a><span class="lineno">  913</span>&#160;};</div>
<div class="line"><a name="l00914"></a><span class="lineno">  914</span>&#160; </div>
<div class="line"><a name="l00915"></a><span class="lineno">  915</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00916"></a><span class="lineno">  916</span>&#160;<span class="keyword">struct </span>bessel_k1e_impl {</div>
<div class="line"><a name="l00917"></a><span class="lineno">  917</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00918"></a><span class="lineno">  918</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T x) {</div>
<div class="line"><a name="l00919"></a><span class="lineno">  919</span>&#160;    <span class="keywordflow">return</span> generic_k1e&lt;T&gt;::run(x);</div>
<div class="line"><a name="l00920"></a><span class="lineno">  920</span>&#160;  }</div>
<div class="line"><a name="l00921"></a><span class="lineno">  921</span>&#160;};</div>
<div class="line"><a name="l00922"></a><span class="lineno">  922</span>&#160; </div>
<div class="line"><a name="l00923"></a><span class="lineno">  923</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00924"></a><span class="lineno">  924</span>&#160;<span class="keyword">struct </span>bessel_k1_retval {</div>
<div class="line"><a name="l00925"></a><span class="lineno">  925</span>&#160;  <span class="keyword">typedef</span> T type;</div>
<div class="line"><a name="l00926"></a><span class="lineno">  926</span>&#160;};</div>
<div class="line"><a name="l00927"></a><span class="lineno">  927</span>&#160; </div>
<div class="line"><a name="l00928"></a><span class="lineno">  928</span>&#160;template &lt;typename T, typename ScalarType = typename unpacket_traits&lt;T&gt;::type&gt;</div>
<div class="line"><a name="l00929"></a><span class="lineno">  929</span>&#160;<span class="keyword">struct </span>generic_k1 {</div>
<div class="line"><a name="l00930"></a><span class="lineno">  930</span>&#160;  EIGEN_STATIC_ASSERT((internal::is_same&lt;T, T&gt;::value == <span class="keyword">false</span>),</div>
<div class="line"><a name="l00931"></a><span class="lineno">  931</span>&#160;                      THIS_TYPE_IS_NOT_SUPPORTED)</div>
<div class="line"><a name="l00932"></a><span class="lineno">  932</span>&#160; </div>
<div class="line"><a name="l00933"></a><span class="lineno">  933</span>&#160;  EIGEN_DEVICE_FUNC <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp;) {</div>
<div class="line"><a name="l00934"></a><span class="lineno">  934</span>&#160;    <span class="keywordflow">return</span> ScalarType(0);</div>
<div class="line"><a name="l00935"></a><span class="lineno">  935</span>&#160;  }</div>
<div class="line"><a name="l00936"></a><span class="lineno">  936</span>&#160;};</div>
<div class="line"><a name="l00937"></a><span class="lineno">  937</span>&#160; </div>
<div class="line"><a name="l00938"></a><span class="lineno">  938</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00939"></a><span class="lineno">  939</span>&#160;<span class="keyword">struct </span>generic_k1&lt;T, float&gt; {</div>
<div class="line"><a name="l00940"></a><span class="lineno">  940</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00941"></a><span class="lineno">  941</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp; x) {</div>
<div class="line"><a name="l00942"></a><span class="lineno">  942</span>&#160;    <span class="comment">/* k1f.c</span></div>
<div class="line"><a name="l00943"></a><span class="lineno">  943</span>&#160;<span class="comment">     *  Modified Bessel function, third kind, order one</span></div>
<div class="line"><a name="l00944"></a><span class="lineno">  944</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00945"></a><span class="lineno">  945</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00946"></a><span class="lineno">  946</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00947"></a><span class="lineno">  947</span>&#160;<span class="comment">     * SYNOPSIS:</span></div>
<div class="line"><a name="l00948"></a><span class="lineno">  948</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00949"></a><span class="lineno">  949</span>&#160;<span class="comment">     * float x, y, k1f();</span></div>
<div class="line"><a name="l00950"></a><span class="lineno">  950</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00951"></a><span class="lineno">  951</span>&#160;<span class="comment">     * y = k1f( x );</span></div>
<div class="line"><a name="l00952"></a><span class="lineno">  952</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00953"></a><span class="lineno">  953</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00954"></a><span class="lineno">  954</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00955"></a><span class="lineno">  955</span>&#160;<span class="comment">     * DESCRIPTION:</span></div>
<div class="line"><a name="l00956"></a><span class="lineno">  956</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00957"></a><span class="lineno">  957</span>&#160;<span class="comment">     * Computes the modified Bessel function of the third kind</span></div>
<div class="line"><a name="l00958"></a><span class="lineno">  958</span>&#160;<span class="comment">     * of order one of the argument.</span></div>
<div class="line"><a name="l00959"></a><span class="lineno">  959</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00960"></a><span class="lineno">  960</span>&#160;<span class="comment">     * The range is partitioned into the two intervals [0,2] and</span></div>
<div class="line"><a name="l00961"></a><span class="lineno">  961</span>&#160;<span class="comment">     * (2, infinity).  Chebyshev polynomial expansions are employed</span></div>
<div class="line"><a name="l00962"></a><span class="lineno">  962</span>&#160;<span class="comment">     * in each interval.</span></div>
<div class="line"><a name="l00963"></a><span class="lineno">  963</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00964"></a><span class="lineno">  964</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00965"></a><span class="lineno">  965</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00966"></a><span class="lineno">  966</span>&#160;<span class="comment">     * ACCURACY:</span></div>
<div class="line"><a name="l00967"></a><span class="lineno">  967</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00968"></a><span class="lineno">  968</span>&#160;<span class="comment">     *                      Relative error:</span></div>
<div class="line"><a name="l00969"></a><span class="lineno">  969</span>&#160;<span class="comment">     * arithmetic   domain     # trials      peak         rms</span></div>
<div class="line"><a name="l00970"></a><span class="lineno">  970</span>&#160;<span class="comment">     *    IEEE      0, 30       30000       4.6e-7      7.6e-8</span></div>
<div class="line"><a name="l00971"></a><span class="lineno">  971</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00972"></a><span class="lineno">  972</span>&#160;<span class="comment">     * ERROR MESSAGES:</span></div>
<div class="line"><a name="l00973"></a><span class="lineno">  973</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00974"></a><span class="lineno">  974</span>&#160;<span class="comment">     *   message         condition      value returned</span></div>
<div class="line"><a name="l00975"></a><span class="lineno">  975</span>&#160;<span class="comment">     * k1 domain          x &lt;= 0          MAXNUM</span></div>
<div class="line"><a name="l00976"></a><span class="lineno">  976</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l00977"></a><span class="lineno">  977</span>&#160;<span class="comment">     */</span></div>
<div class="line"><a name="l00978"></a><span class="lineno">  978</span>&#160; </div>
<div class="line"><a name="l00979"></a><span class="lineno">  979</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> A[] = {-2.21338763073472585583E-8f, -2.43340614156596823496E-6f,</div>
<div class="line"><a name="l00980"></a><span class="lineno">  980</span>&#160;                        -1.73028895751305206302E-4f, -6.97572385963986435018E-3f,</div>
<div class="line"><a name="l00981"></a><span class="lineno">  981</span>&#160;                        -1.22611180822657148235E-1f, -3.53155960776544875667E-1f,</div>
<div class="line"><a name="l00982"></a><span class="lineno">  982</span>&#160;                        1.52530022733894777053E0f};</div>
<div class="line"><a name="l00983"></a><span class="lineno">  983</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> B[] = {2.01504975519703286596E-9f, -1.03457624656780970260E-8f,</div>
<div class="line"><a name="l00984"></a><span class="lineno">  984</span>&#160;                       5.74108412545004946722E-8f, -3.50196060308781257119E-7f,</div>
<div class="line"><a name="l00985"></a><span class="lineno">  985</span>&#160;                       2.40648494783721712015E-6f, -1.93619797416608296024E-5f,</div>
<div class="line"><a name="l00986"></a><span class="lineno">  986</span>&#160;                       1.95215518471351631108E-4f, -2.85781685962277938680E-3f,</div>
<div class="line"><a name="l00987"></a><span class="lineno">  987</span>&#160;                       1.03923736576817238437E-1f, 2.72062619048444266945E0f};</div>
<div class="line"><a name="l00988"></a><span class="lineno">  988</span>&#160;    <span class="keyword">const</span> T MAXNUM = pset1&lt;T&gt;(NumTraits&lt;float&gt;::infinity());</div>
<div class="line"><a name="l00989"></a><span class="lineno">  989</span>&#160;    <span class="keyword">const</span> T two = pset1&lt;T&gt;(2.0);</div>
<div class="line"><a name="l00990"></a><span class="lineno">  990</span>&#160;    T x_le_two = pdiv(internal::pchebevl&lt;T, 7&gt;::run(</div>
<div class="line"><a name="l00991"></a><span class="lineno">  991</span>&#160;        pmadd(x, x, pset1&lt;T&gt;(-2.0)), A), x);</div>
<div class="line"><a name="l00992"></a><span class="lineno">  992</span>&#160;    x_le_two = pmadd(</div>
<div class="line"><a name="l00993"></a><span class="lineno">  993</span>&#160;        generic_i1&lt;T, float&gt;::run(x), plog(pmul(pset1&lt;T&gt;(0.5), x)), x_le_two);</div>
<div class="line"><a name="l00994"></a><span class="lineno">  994</span>&#160;    x_le_two = pselect(pcmp_le(x, pset1&lt;T&gt;(0.0)), MAXNUM, x_le_two);</div>
<div class="line"><a name="l00995"></a><span class="lineno">  995</span>&#160;    T x_gt_two = pmul(</div>
<div class="line"><a name="l00996"></a><span class="lineno">  996</span>&#160;        pexp(pnegate(x)),</div>
<div class="line"><a name="l00997"></a><span class="lineno">  997</span>&#160;        pmul(</div>
<div class="line"><a name="l00998"></a><span class="lineno">  998</span>&#160;            internal::pchebevl&lt;T, 10&gt;::run(</div>
<div class="line"><a name="l00999"></a><span class="lineno">  999</span>&#160;                psub(pdiv(pset1&lt;T&gt;(8.0), x), two), B),</div>
<div class="line"><a name="l01000"></a><span class="lineno"> 1000</span>&#160;            prsqrt(x)));</div>
<div class="line"><a name="l01001"></a><span class="lineno"> 1001</span>&#160;    <span class="keywordflow">return</span> pselect(pcmp_le(x, two), x_le_two, x_gt_two);</div>
<div class="line"><a name="l01002"></a><span class="lineno"> 1002</span>&#160;  }</div>
<div class="line"><a name="l01003"></a><span class="lineno"> 1003</span>&#160;};</div>
<div class="line"><a name="l01004"></a><span class="lineno"> 1004</span>&#160; </div>
<div class="line"><a name="l01005"></a><span class="lineno"> 1005</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l01006"></a><span class="lineno"> 1006</span>&#160;<span class="keyword">struct </span>generic_k1&lt;T, double&gt; {</div>
<div class="line"><a name="l01007"></a><span class="lineno"> 1007</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l01008"></a><span class="lineno"> 1008</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp; x) {</div>
<div class="line"><a name="l01009"></a><span class="lineno"> 1009</span>&#160;    <span class="comment">/*  k1.c</span></div>
<div class="line"><a name="l01010"></a><span class="lineno"> 1010</span>&#160;<span class="comment">     *  Modified Bessel function, third kind, order one</span></div>
<div class="line"><a name="l01011"></a><span class="lineno"> 1011</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01012"></a><span class="lineno"> 1012</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01013"></a><span class="lineno"> 1013</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01014"></a><span class="lineno"> 1014</span>&#160;<span class="comment">     * SYNOPSIS:</span></div>
<div class="line"><a name="l01015"></a><span class="lineno"> 1015</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01016"></a><span class="lineno"> 1016</span>&#160;<span class="comment">     * float x, y, k1f();</span></div>
<div class="line"><a name="l01017"></a><span class="lineno"> 1017</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01018"></a><span class="lineno"> 1018</span>&#160;<span class="comment">     * y = k1f( x );</span></div>
<div class="line"><a name="l01019"></a><span class="lineno"> 1019</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01020"></a><span class="lineno"> 1020</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01021"></a><span class="lineno"> 1021</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01022"></a><span class="lineno"> 1022</span>&#160;<span class="comment">     * DESCRIPTION:</span></div>
<div class="line"><a name="l01023"></a><span class="lineno"> 1023</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01024"></a><span class="lineno"> 1024</span>&#160;<span class="comment">     * Computes the modified Bessel function of the third kind</span></div>
<div class="line"><a name="l01025"></a><span class="lineno"> 1025</span>&#160;<span class="comment">     * of order one of the argument.</span></div>
<div class="line"><a name="l01026"></a><span class="lineno"> 1026</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01027"></a><span class="lineno"> 1027</span>&#160;<span class="comment">     * The range is partitioned into the two intervals [0,2] and</span></div>
<div class="line"><a name="l01028"></a><span class="lineno"> 1028</span>&#160;<span class="comment">     * (2, infinity).  Chebyshev polynomial expansions are employed</span></div>
<div class="line"><a name="l01029"></a><span class="lineno"> 1029</span>&#160;<span class="comment">     * in each interval.</span></div>
<div class="line"><a name="l01030"></a><span class="lineno"> 1030</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01031"></a><span class="lineno"> 1031</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01032"></a><span class="lineno"> 1032</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01033"></a><span class="lineno"> 1033</span>&#160;<span class="comment">     * ACCURACY:</span></div>
<div class="line"><a name="l01034"></a><span class="lineno"> 1034</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01035"></a><span class="lineno"> 1035</span>&#160;<span class="comment">     *                      Relative error:</span></div>
<div class="line"><a name="l01036"></a><span class="lineno"> 1036</span>&#160;<span class="comment">     * arithmetic   domain     # trials      peak         rms</span></div>
<div class="line"><a name="l01037"></a><span class="lineno"> 1037</span>&#160;<span class="comment">     *    IEEE      0, 30       30000       4.6e-7      7.6e-8</span></div>
<div class="line"><a name="l01038"></a><span class="lineno"> 1038</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01039"></a><span class="lineno"> 1039</span>&#160;<span class="comment">     * ERROR MESSAGES:</span></div>
<div class="line"><a name="l01040"></a><span class="lineno"> 1040</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01041"></a><span class="lineno"> 1041</span>&#160;<span class="comment">     *   message         condition      value returned</span></div>
<div class="line"><a name="l01042"></a><span class="lineno"> 1042</span>&#160;<span class="comment">     * k1 domain          x &lt;= 0          MAXNUM</span></div>
<div class="line"><a name="l01043"></a><span class="lineno"> 1043</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01044"></a><span class="lineno"> 1044</span>&#160;<span class="comment">     */</span></div>
<div class="line"><a name="l01045"></a><span class="lineno"> 1045</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> A[] = {-7.02386347938628759343E-18, -2.42744985051936593393E-15,</div>
<div class="line"><a name="l01046"></a><span class="lineno"> 1046</span>&#160;                        -6.66690169419932900609E-13, -1.41148839263352776110E-10,</div>
<div class="line"><a name="l01047"></a><span class="lineno"> 1047</span>&#160;                        -2.21338763073472585583E-8, -2.43340614156596823496E-6,</div>
<div class="line"><a name="l01048"></a><span class="lineno"> 1048</span>&#160;                        -1.73028895751305206302E-4, -6.97572385963986435018E-3,</div>
<div class="line"><a name="l01049"></a><span class="lineno"> 1049</span>&#160;                        -1.22611180822657148235E-1, -3.53155960776544875667E-1,</div>
<div class="line"><a name="l01050"></a><span class="lineno"> 1050</span>&#160;                        1.52530022733894777053E0};</div>
<div class="line"><a name="l01051"></a><span class="lineno"> 1051</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> B[] = {-5.75674448366501715755E-18, 1.79405087314755922667E-17,</div>
<div class="line"><a name="l01052"></a><span class="lineno"> 1052</span>&#160;                        -5.68946255844285935196E-17, 1.83809354436663880070E-16,</div>
<div class="line"><a name="l01053"></a><span class="lineno"> 1053</span>&#160;                        -6.05704724837331885336E-16, 2.03870316562433424052E-15,</div>
<div class="line"><a name="l01054"></a><span class="lineno"> 1054</span>&#160;                        -7.01983709041831346144E-15, 2.47715442448130437068E-14,</div>
<div class="line"><a name="l01055"></a><span class="lineno"> 1055</span>&#160;                        -8.97670518232499435011E-14, 3.34841966607842919884E-13,</div>
<div class="line"><a name="l01056"></a><span class="lineno"> 1056</span>&#160;                        -1.28917396095102890680E-12, 5.13963967348173025100E-12,</div>
<div class="line"><a name="l01057"></a><span class="lineno"> 1057</span>&#160;                        -2.12996783842756842877E-11, 9.21831518760500529508E-11,</div>
<div class="line"><a name="l01058"></a><span class="lineno"> 1058</span>&#160;                        -4.19035475934189648750E-10, 2.01504975519703286596E-9,</div>
<div class="line"><a name="l01059"></a><span class="lineno"> 1059</span>&#160;                        -1.03457624656780970260E-8, 5.74108412545004946722E-8,</div>
<div class="line"><a name="l01060"></a><span class="lineno"> 1060</span>&#160;                        -3.50196060308781257119E-7, 2.40648494783721712015E-6,</div>
<div class="line"><a name="l01061"></a><span class="lineno"> 1061</span>&#160;                        -1.93619797416608296024E-5, 1.95215518471351631108E-4,</div>
<div class="line"><a name="l01062"></a><span class="lineno"> 1062</span>&#160;                        -2.85781685962277938680E-3, 1.03923736576817238437E-1,</div>
<div class="line"><a name="l01063"></a><span class="lineno"> 1063</span>&#160;                        2.72062619048444266945E0};</div>
<div class="line"><a name="l01064"></a><span class="lineno"> 1064</span>&#160;    <span class="keyword">const</span> T MAXNUM = pset1&lt;T&gt;(NumTraits&lt;double&gt;::infinity());</div>
<div class="line"><a name="l01065"></a><span class="lineno"> 1065</span>&#160;    <span class="keyword">const</span> T two = pset1&lt;T&gt;(2.0);</div>
<div class="line"><a name="l01066"></a><span class="lineno"> 1066</span>&#160;    T x_le_two = pdiv(internal::pchebevl&lt;T, 11&gt;::run(</div>
<div class="line"><a name="l01067"></a><span class="lineno"> 1067</span>&#160;        pmadd(x, x, pset1&lt;T&gt;(-2.0)), A), x);</div>
<div class="line"><a name="l01068"></a><span class="lineno"> 1068</span>&#160;    x_le_two = pmadd(</div>
<div class="line"><a name="l01069"></a><span class="lineno"> 1069</span>&#160;        generic_i1&lt;T, double&gt;::run(x), plog(pmul(pset1&lt;T&gt;(0.5), x)), x_le_two);</div>
<div class="line"><a name="l01070"></a><span class="lineno"> 1070</span>&#160;    x_le_two = pselect(pcmp_le(x, pset1&lt;T&gt;(0.0)), MAXNUM, x_le_two);</div>
<div class="line"><a name="l01071"></a><span class="lineno"> 1071</span>&#160;    T x_gt_two = pmul(</div>
<div class="line"><a name="l01072"></a><span class="lineno"> 1072</span>&#160;        pexp(-x),</div>
<div class="line"><a name="l01073"></a><span class="lineno"> 1073</span>&#160;        pmul(</div>
<div class="line"><a name="l01074"></a><span class="lineno"> 1074</span>&#160;            internal::pchebevl&lt;T, 25&gt;::run(</div>
<div class="line"><a name="l01075"></a><span class="lineno"> 1075</span>&#160;                psub(pdiv(pset1&lt;T&gt;(8.0), x), two), B),</div>
<div class="line"><a name="l01076"></a><span class="lineno"> 1076</span>&#160;            prsqrt(x)));</div>
<div class="line"><a name="l01077"></a><span class="lineno"> 1077</span>&#160;    <span class="keywordflow">return</span> pselect(pcmp_le(x, two), x_le_two, x_gt_two);</div>
<div class="line"><a name="l01078"></a><span class="lineno"> 1078</span>&#160;  }</div>
<div class="line"><a name="l01079"></a><span class="lineno"> 1079</span>&#160;};</div>
<div class="line"><a name="l01080"></a><span class="lineno"> 1080</span>&#160; </div>
<div class="line"><a name="l01081"></a><span class="lineno"> 1081</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l01082"></a><span class="lineno"> 1082</span>&#160;<span class="keyword">struct </span>bessel_k1_impl {</div>
<div class="line"><a name="l01083"></a><span class="lineno"> 1083</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l01084"></a><span class="lineno"> 1084</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T x) {</div>
<div class="line"><a name="l01085"></a><span class="lineno"> 1085</span>&#160;    <span class="keywordflow">return</span> generic_k1&lt;T&gt;::run(x);</div>
<div class="line"><a name="l01086"></a><span class="lineno"> 1086</span>&#160;  }</div>
<div class="line"><a name="l01087"></a><span class="lineno"> 1087</span>&#160;};</div>
<div class="line"><a name="l01088"></a><span class="lineno"> 1088</span>&#160; </div>
<div class="line"><a name="l01089"></a><span class="lineno"> 1089</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l01090"></a><span class="lineno"> 1090</span>&#160;<span class="keyword">struct </span>bessel_j0_retval {</div>
<div class="line"><a name="l01091"></a><span class="lineno"> 1091</span>&#160;  <span class="keyword">typedef</span> T type;</div>
<div class="line"><a name="l01092"></a><span class="lineno"> 1092</span>&#160;};</div>
<div class="line"><a name="l01093"></a><span class="lineno"> 1093</span>&#160; </div>
<div class="line"><a name="l01094"></a><span class="lineno"> 1094</span>&#160;template &lt;typename T, typename ScalarType = typename unpacket_traits&lt;T&gt;::type&gt;</div>
<div class="line"><a name="l01095"></a><span class="lineno"> 1095</span>&#160;<span class="keyword">struct </span>generic_j0 {</div>
<div class="line"><a name="l01096"></a><span class="lineno"> 1096</span>&#160;  EIGEN_STATIC_ASSERT((internal::is_same&lt;T, T&gt;::value == <span class="keyword">false</span>),</div>
<div class="line"><a name="l01097"></a><span class="lineno"> 1097</span>&#160;                      THIS_TYPE_IS_NOT_SUPPORTED)</div>
<div class="line"><a name="l01098"></a><span class="lineno"> 1098</span>&#160; </div>
<div class="line"><a name="l01099"></a><span class="lineno"> 1099</span>&#160;  EIGEN_DEVICE_FUNC <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp;) {</div>
<div class="line"><a name="l01100"></a><span class="lineno"> 1100</span>&#160;    <span class="keywordflow">return</span> ScalarType(0);</div>
<div class="line"><a name="l01101"></a><span class="lineno"> 1101</span>&#160;  }</div>
<div class="line"><a name="l01102"></a><span class="lineno"> 1102</span>&#160;};</div>
<div class="line"><a name="l01103"></a><span class="lineno"> 1103</span>&#160; </div>
<div class="line"><a name="l01104"></a><span class="lineno"> 1104</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l01105"></a><span class="lineno"> 1105</span>&#160;<span class="keyword">struct </span>generic_j0&lt;T, float&gt; {</div>
<div class="line"><a name="l01106"></a><span class="lineno"> 1106</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l01107"></a><span class="lineno"> 1107</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp; x) {</div>
<div class="line"><a name="l01108"></a><span class="lineno"> 1108</span>&#160;    <span class="comment">/* j0f.c</span></div>
<div class="line"><a name="l01109"></a><span class="lineno"> 1109</span>&#160;<span class="comment">     *  Bessel function of order zero</span></div>
<div class="line"><a name="l01110"></a><span class="lineno"> 1110</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01111"></a><span class="lineno"> 1111</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01112"></a><span class="lineno"> 1112</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01113"></a><span class="lineno"> 1113</span>&#160;<span class="comment">     * SYNOPSIS:</span></div>
<div class="line"><a name="l01114"></a><span class="lineno"> 1114</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01115"></a><span class="lineno"> 1115</span>&#160;<span class="comment">     * float x, y, j0f();</span></div>
<div class="line"><a name="l01116"></a><span class="lineno"> 1116</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01117"></a><span class="lineno"> 1117</span>&#160;<span class="comment">     * y = j0f( x );</span></div>
<div class="line"><a name="l01118"></a><span class="lineno"> 1118</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01119"></a><span class="lineno"> 1119</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01120"></a><span class="lineno"> 1120</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01121"></a><span class="lineno"> 1121</span>&#160;<span class="comment">     * DESCRIPTION:</span></div>
<div class="line"><a name="l01122"></a><span class="lineno"> 1122</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01123"></a><span class="lineno"> 1123</span>&#160;<span class="comment">     * Returns Bessel function of order zero of the argument.</span></div>
<div class="line"><a name="l01124"></a><span class="lineno"> 1124</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01125"></a><span class="lineno"> 1125</span>&#160;<span class="comment">     * The domain is divided into the intervals [0, 2] and</span></div>
<div class="line"><a name="l01126"></a><span class="lineno"> 1126</span>&#160;<span class="comment">     * (2, infinity). In the first interval the following polynomial</span></div>
<div class="line"><a name="l01127"></a><span class="lineno"> 1127</span>&#160;<span class="comment">     * approximation is used:</span></div>
<div class="line"><a name="l01128"></a><span class="lineno"> 1128</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01129"></a><span class="lineno"> 1129</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01130"></a><span class="lineno"> 1130</span>&#160;<span class="comment">     *        2         2         2</span></div>
<div class="line"><a name="l01131"></a><span class="lineno"> 1131</span>&#160;<span class="comment">     * (w - r  ) (w - r  ) (w - r  ) P(w)</span></div>
<div class="line"><a name="l01132"></a><span class="lineno"> 1132</span>&#160;<span class="comment">     *       1         2         3</span></div>
<div class="line"><a name="l01133"></a><span class="lineno"> 1133</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01134"></a><span class="lineno"> 1134</span>&#160;<span class="comment">     *            2</span></div>
<div class="line"><a name="l01135"></a><span class="lineno"> 1135</span>&#160;<span class="comment">     * where w = x  and the three r&#39;s are zeros of the function.</span></div>
<div class="line"><a name="l01136"></a><span class="lineno"> 1136</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01137"></a><span class="lineno"> 1137</span>&#160;<span class="comment">     * In the second interval, the modulus and phase are approximated</span></div>
<div class="line"><a name="l01138"></a><span class="lineno"> 1138</span>&#160;<span class="comment">     * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)</span></div>
<div class="line"><a name="l01139"></a><span class="lineno"> 1139</span>&#160;<span class="comment">     * and Phase(x) = x + 1/x R(1/x^2) - pi/4.  The function is</span></div>
<div class="line"><a name="l01140"></a><span class="lineno"> 1140</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01141"></a><span class="lineno"> 1141</span>&#160;<span class="comment">     *   j0(x) = Modulus(x) cos( Phase(x) ).</span></div>
<div class="line"><a name="l01142"></a><span class="lineno"> 1142</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01143"></a><span class="lineno"> 1143</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01144"></a><span class="lineno"> 1144</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01145"></a><span class="lineno"> 1145</span>&#160;<span class="comment">     * ACCURACY:</span></div>
<div class="line"><a name="l01146"></a><span class="lineno"> 1146</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01147"></a><span class="lineno"> 1147</span>&#160;<span class="comment">     *                      Absolute error:</span></div>
<div class="line"><a name="l01148"></a><span class="lineno"> 1148</span>&#160;<span class="comment">     * arithmetic   domain     # trials      peak         rms</span></div>
<div class="line"><a name="l01149"></a><span class="lineno"> 1149</span>&#160;<span class="comment">     *    IEEE      0, 2        100000      1.3e-7      3.6e-8</span></div>
<div class="line"><a name="l01150"></a><span class="lineno"> 1150</span>&#160;<span class="comment">     *    IEEE      2, 32       100000      1.9e-7      5.4e-8</span></div>
<div class="line"><a name="l01151"></a><span class="lineno"> 1151</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01152"></a><span class="lineno"> 1152</span>&#160;<span class="comment">     */</span></div>
<div class="line"><a name="l01153"></a><span class="lineno"> 1153</span>&#160; </div>
<div class="line"><a name="l01154"></a><span class="lineno"> 1154</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> JP[] = {-6.068350350393235E-008f, 6.388945720783375E-006f,</div>
<div class="line"><a name="l01155"></a><span class="lineno"> 1155</span>&#160;                        -3.969646342510940E-004f, 1.332913422519003E-002f,</div>
<div class="line"><a name="l01156"></a><span class="lineno"> 1156</span>&#160;                        -1.729150680240724E-001f};</div>
<div class="line"><a name="l01157"></a><span class="lineno"> 1157</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> MO[] = {-6.838999669318810E-002f, 1.864949361379502E-001f,</div>
<div class="line"><a name="l01158"></a><span class="lineno"> 1158</span>&#160;                        -2.145007480346739E-001f, 1.197549369473540E-001f,</div>
<div class="line"><a name="l01159"></a><span class="lineno"> 1159</span>&#160;                        -3.560281861530129E-003f, -4.969382655296620E-002f,</div>
<div class="line"><a name="l01160"></a><span class="lineno"> 1160</span>&#160;                        -3.355424622293709E-006f, 7.978845717621440E-001f};</div>
<div class="line"><a name="l01161"></a><span class="lineno"> 1161</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> PH[] = {3.242077816988247E+001f, -3.630592630518434E+001f,</div>
<div class="line"><a name="l01162"></a><span class="lineno"> 1162</span>&#160;                        1.756221482109099E+001f, -4.974978466280903E+000f,</div>
<div class="line"><a name="l01163"></a><span class="lineno"> 1163</span>&#160;                        1.001973420681837E+000f, -1.939906941791308E-001f,</div>
<div class="line"><a name="l01164"></a><span class="lineno"> 1164</span>&#160;                        6.490598792654666E-002f, -1.249992184872738E-001f};</div>
<div class="line"><a name="l01165"></a><span class="lineno"> 1165</span>&#160;    <span class="keyword">const</span> T DR1 =  pset1&lt;T&gt;(5.78318596294678452118f);</div>
<div class="line"><a name="l01166"></a><span class="lineno"> 1166</span>&#160;    <span class="keyword">const</span> T NEG_PIO4F = pset1&lt;T&gt;(-0.7853981633974483096f); <span class="comment">/* -pi / 4 */</span></div>
<div class="line"><a name="l01167"></a><span class="lineno"> 1167</span>&#160;    T y = pabs(x);</div>
<div class="line"><a name="l01168"></a><span class="lineno"> 1168</span>&#160;    T z = pmul(y, y);</div>
<div class="line"><a name="l01169"></a><span class="lineno"> 1169</span>&#160;    T y_le_two = pselect(</div>
<div class="line"><a name="l01170"></a><span class="lineno"> 1170</span>&#160;        pcmp_lt(y, pset1&lt;T&gt;(1.0e-3f)),</div>
<div class="line"><a name="l01171"></a><span class="lineno"> 1171</span>&#160;        pmadd(z, pset1&lt;T&gt;(-0.25f), pset1&lt;T&gt;(1.0f)),</div>
<div class="line"><a name="l01172"></a><span class="lineno"> 1172</span>&#160;        pmul(psub(z, DR1), internal::ppolevl&lt;T, 4&gt;::run(z, JP)));</div>
<div class="line"><a name="l01173"></a><span class="lineno"> 1173</span>&#160;    T q = pdiv(pset1&lt;T&gt;(1.0f), y);</div>
<div class="line"><a name="l01174"></a><span class="lineno"> 1174</span>&#160;    T w = prsqrt(y);</div>
<div class="line"><a name="l01175"></a><span class="lineno"> 1175</span>&#160;    T p = pmul(w, internal::ppolevl&lt;T, 7&gt;::run(q, MO));</div>
<div class="line"><a name="l01176"></a><span class="lineno"> 1176</span>&#160;    w = pmul(q, q);</div>
<div class="line"><a name="l01177"></a><span class="lineno"> 1177</span>&#160;    T yn = pmadd(q, internal::ppolevl&lt;T, 7&gt;::run(w, PH), NEG_PIO4F);</div>
<div class="line"><a name="l01178"></a><span class="lineno"> 1178</span>&#160;    T y_gt_two = pmul(p, pcos(padd(yn, y)));</div>
<div class="line"><a name="l01179"></a><span class="lineno"> 1179</span>&#160;    <span class="keywordflow">return</span> pselect(pcmp_le(y, pset1&lt;T&gt;(2.0)), y_le_two, y_gt_two);</div>
<div class="line"><a name="l01180"></a><span class="lineno"> 1180</span>&#160;  }</div>
<div class="line"><a name="l01181"></a><span class="lineno"> 1181</span>&#160;};</div>
<div class="line"><a name="l01182"></a><span class="lineno"> 1182</span>&#160; </div>
<div class="line"><a name="l01183"></a><span class="lineno"> 1183</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l01184"></a><span class="lineno"> 1184</span>&#160;<span class="keyword">struct </span>generic_j0&lt;T, double&gt; {</div>
<div class="line"><a name="l01185"></a><span class="lineno"> 1185</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l01186"></a><span class="lineno"> 1186</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp; x) {</div>
<div class="line"><a name="l01187"></a><span class="lineno"> 1187</span>&#160;    <span class="comment">/*  j0.c</span></div>
<div class="line"><a name="l01188"></a><span class="lineno"> 1188</span>&#160;<span class="comment">     *  Bessel function of order zero</span></div>
<div class="line"><a name="l01189"></a><span class="lineno"> 1189</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01190"></a><span class="lineno"> 1190</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01191"></a><span class="lineno"> 1191</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01192"></a><span class="lineno"> 1192</span>&#160;<span class="comment">     * SYNOPSIS:</span></div>
<div class="line"><a name="l01193"></a><span class="lineno"> 1193</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01194"></a><span class="lineno"> 1194</span>&#160;<span class="comment">     * double x, y, j0();</span></div>
<div class="line"><a name="l01195"></a><span class="lineno"> 1195</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01196"></a><span class="lineno"> 1196</span>&#160;<span class="comment">     * y = j0( x );</span></div>
<div class="line"><a name="l01197"></a><span class="lineno"> 1197</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01198"></a><span class="lineno"> 1198</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01199"></a><span class="lineno"> 1199</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01200"></a><span class="lineno"> 1200</span>&#160;<span class="comment">     * DESCRIPTION:</span></div>
<div class="line"><a name="l01201"></a><span class="lineno"> 1201</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01202"></a><span class="lineno"> 1202</span>&#160;<span class="comment">     * Returns Bessel function of order zero of the argument.</span></div>
<div class="line"><a name="l01203"></a><span class="lineno"> 1203</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01204"></a><span class="lineno"> 1204</span>&#160;<span class="comment">     * The domain is divided into the intervals [0, 5] and</span></div>
<div class="line"><a name="l01205"></a><span class="lineno"> 1205</span>&#160;<span class="comment">     * (5, infinity). In the first interval the following rational</span></div>
<div class="line"><a name="l01206"></a><span class="lineno"> 1206</span>&#160;<span class="comment">     * approximation is used:</span></div>
<div class="line"><a name="l01207"></a><span class="lineno"> 1207</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01208"></a><span class="lineno"> 1208</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01209"></a><span class="lineno"> 1209</span>&#160;<span class="comment">     *        2         2</span></div>
<div class="line"><a name="l01210"></a><span class="lineno"> 1210</span>&#160;<span class="comment">     * (w - r  ) (w - r  ) P (w) / Q (w)</span></div>
<div class="line"><a name="l01211"></a><span class="lineno"> 1211</span>&#160;<span class="comment">     *       1         2    3       8</span></div>
<div class="line"><a name="l01212"></a><span class="lineno"> 1212</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01213"></a><span class="lineno"> 1213</span>&#160;<span class="comment">     *            2</span></div>
<div class="line"><a name="l01214"></a><span class="lineno"> 1214</span>&#160;<span class="comment">     * where w = x  and the two r&#39;s are zeros of the function.</span></div>
<div class="line"><a name="l01215"></a><span class="lineno"> 1215</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01216"></a><span class="lineno"> 1216</span>&#160;<span class="comment">     * In the second interval, the Hankel asymptotic expansion</span></div>
<div class="line"><a name="l01217"></a><span class="lineno"> 1217</span>&#160;<span class="comment">     * is employed with two rational functions of degree 6/6</span></div>
<div class="line"><a name="l01218"></a><span class="lineno"> 1218</span>&#160;<span class="comment">     * and 7/7.</span></div>
<div class="line"><a name="l01219"></a><span class="lineno"> 1219</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01220"></a><span class="lineno"> 1220</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01221"></a><span class="lineno"> 1221</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01222"></a><span class="lineno"> 1222</span>&#160;<span class="comment">     * ACCURACY:</span></div>
<div class="line"><a name="l01223"></a><span class="lineno"> 1223</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01224"></a><span class="lineno"> 1224</span>&#160;<span class="comment">     *                      Absolute error:</span></div>
<div class="line"><a name="l01225"></a><span class="lineno"> 1225</span>&#160;<span class="comment">     * arithmetic   domain     # trials      peak         rms</span></div>
<div class="line"><a name="l01226"></a><span class="lineno"> 1226</span>&#160;<span class="comment">     *    DEC       0, 30       10000       4.4e-17     6.3e-18</span></div>
<div class="line"><a name="l01227"></a><span class="lineno"> 1227</span>&#160;<span class="comment">     *    IEEE      0, 30       60000       4.2e-16     1.1e-16</span></div>
<div class="line"><a name="l01228"></a><span class="lineno"> 1228</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01229"></a><span class="lineno"> 1229</span>&#160;<span class="comment">     */</span></div>
<div class="line"><a name="l01230"></a><span class="lineno"> 1230</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> PP[] = {7.96936729297347051624E-4, 8.28352392107440799803E-2,</div>
<div class="line"><a name="l01231"></a><span class="lineno"> 1231</span>&#160;                        1.23953371646414299388E0, 5.44725003058768775090E0,</div>
<div class="line"><a name="l01232"></a><span class="lineno"> 1232</span>&#160;                        8.74716500199817011941E0, 5.30324038235394892183E0,</div>
<div class="line"><a name="l01233"></a><span class="lineno"> 1233</span>&#160;                        9.99999999999999997821E-1};</div>
<div class="line"><a name="l01234"></a><span class="lineno"> 1234</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> PQ[] = {9.24408810558863637013E-4, 8.56288474354474431428E-2,</div>
<div class="line"><a name="l01235"></a><span class="lineno"> 1235</span>&#160;                         1.25352743901058953537E0, 5.47097740330417105182E0,</div>
<div class="line"><a name="l01236"></a><span class="lineno"> 1236</span>&#160;                         8.76190883237069594232E0, 5.30605288235394617618E0,</div>
<div class="line"><a name="l01237"></a><span class="lineno"> 1237</span>&#160;                         1.00000000000000000218E0};</div>
<div class="line"><a name="l01238"></a><span class="lineno"> 1238</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> QP[] = {-1.13663838898469149931E-2, -1.28252718670509318512E0,</div>
<div class="line"><a name="l01239"></a><span class="lineno"> 1239</span>&#160;                         -1.95539544257735972385E1, -9.32060152123768231369E1,</div>
<div class="line"><a name="l01240"></a><span class="lineno"> 1240</span>&#160;                         -1.77681167980488050595E2, -1.47077505154951170175E2,</div>
<div class="line"><a name="l01241"></a><span class="lineno"> 1241</span>&#160;                         -5.14105326766599330220E1, -6.05014350600728481186E0};</div>
<div class="line"><a name="l01242"></a><span class="lineno"> 1242</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> QQ[] = {1.00000000000000000000E0, 6.43178256118178023184E1,</div>
<div class="line"><a name="l01243"></a><span class="lineno"> 1243</span>&#160;                         8.56430025976980587198E2, 3.88240183605401609683E3,</div>
<div class="line"><a name="l01244"></a><span class="lineno"> 1244</span>&#160;                         7.24046774195652478189E3, 5.93072701187316984827E3,</div>
<div class="line"><a name="l01245"></a><span class="lineno"> 1245</span>&#160;                         2.06209331660327847417E3, 2.42005740240291393179E2};</div>
<div class="line"><a name="l01246"></a><span class="lineno"> 1246</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> RP[] = {-4.79443220978201773821E9, 1.95617491946556577543E12,</div>
<div class="line"><a name="l01247"></a><span class="lineno"> 1247</span>&#160;                         -2.49248344360967716204E14, 9.70862251047306323952E15};</div>
<div class="line"><a name="l01248"></a><span class="lineno"> 1248</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> RQ[] = {1.00000000000000000000E0, 4.99563147152651017219E2,</div>
<div class="line"><a name="l01249"></a><span class="lineno"> 1249</span>&#160;                         1.73785401676374683123E5, 4.84409658339962045305E7,</div>
<div class="line"><a name="l01250"></a><span class="lineno"> 1250</span>&#160;                         1.11855537045356834862E10, 2.11277520115489217587E12,</div>
<div class="line"><a name="l01251"></a><span class="lineno"> 1251</span>&#160;                         3.10518229857422583814E14, 3.18121955943204943306E16,</div>
<div class="line"><a name="l01252"></a><span class="lineno"> 1252</span>&#160;                         1.71086294081043136091E18};</div>
<div class="line"><a name="l01253"></a><span class="lineno"> 1253</span>&#160;    <span class="keyword">const</span> T DR1 = pset1&lt;T&gt;(5.78318596294678452118E0);</div>
<div class="line"><a name="l01254"></a><span class="lineno"> 1254</span>&#160;    <span class="keyword">const</span> T DR2 = pset1&lt;T&gt;(3.04712623436620863991E1);</div>
<div class="line"><a name="l01255"></a><span class="lineno"> 1255</span>&#160;    <span class="keyword">const</span> T SQ2OPI = pset1&lt;T&gt;(7.9788456080286535587989E-1); <span class="comment">/* sqrt(2 / pi) */</span></div>
<div class="line"><a name="l01256"></a><span class="lineno"> 1256</span>&#160;    <span class="keyword">const</span> T NEG_PIO4 = pset1&lt;T&gt;(-0.7853981633974483096); <span class="comment">/* pi / 4 */</span></div>
<div class="line"><a name="l01257"></a><span class="lineno"> 1257</span>&#160; </div>
<div class="line"><a name="l01258"></a><span class="lineno"> 1258</span>&#160;    T y = pabs(x);</div>
<div class="line"><a name="l01259"></a><span class="lineno"> 1259</span>&#160;    T z = pmul(y, y);</div>
<div class="line"><a name="l01260"></a><span class="lineno"> 1260</span>&#160;    T y_le_five = pselect(</div>
<div class="line"><a name="l01261"></a><span class="lineno"> 1261</span>&#160;        pcmp_lt(y, pset1&lt;T&gt;(1.0e-5)),</div>
<div class="line"><a name="l01262"></a><span class="lineno"> 1262</span>&#160;        pmadd(z, pset1&lt;T&gt;(-0.25), pset1&lt;T&gt;(1.0)),</div>
<div class="line"><a name="l01263"></a><span class="lineno"> 1263</span>&#160;        pmul(pmul(psub(z, DR1), psub(z, DR2)),</div>
<div class="line"><a name="l01264"></a><span class="lineno"> 1264</span>&#160;             pdiv(internal::ppolevl&lt;T, 3&gt;::run(z, RP),</div>
<div class="line"><a name="l01265"></a><span class="lineno"> 1265</span>&#160;                  internal::ppolevl&lt;T, 8&gt;::run(z, RQ))));</div>
<div class="line"><a name="l01266"></a><span class="lineno"> 1266</span>&#160;    T s = pdiv(pset1&lt;T&gt;(25.0), z);</div>
<div class="line"><a name="l01267"></a><span class="lineno"> 1267</span>&#160;    T p = pdiv(</div>
<div class="line"><a name="l01268"></a><span class="lineno"> 1268</span>&#160;        internal::ppolevl&lt;T, 6&gt;::run(s, PP),</div>
<div class="line"><a name="l01269"></a><span class="lineno"> 1269</span>&#160;        internal::ppolevl&lt;T, 6&gt;::run(s, PQ));</div>
<div class="line"><a name="l01270"></a><span class="lineno"> 1270</span>&#160;    T q = pdiv(</div>
<div class="line"><a name="l01271"></a><span class="lineno"> 1271</span>&#160;        internal::ppolevl&lt;T, 7&gt;::run(s, QP),</div>
<div class="line"><a name="l01272"></a><span class="lineno"> 1272</span>&#160;        internal::ppolevl&lt;T, 7&gt;::run(s, QQ));</div>
<div class="line"><a name="l01273"></a><span class="lineno"> 1273</span>&#160;    T yn = padd(y, NEG_PIO4);</div>
<div class="line"><a name="l01274"></a><span class="lineno"> 1274</span>&#160;    T w = pdiv(pset1&lt;T&gt;(-5.0), y);</div>
<div class="line"><a name="l01275"></a><span class="lineno"> 1275</span>&#160;    p = pmadd(p, pcos(yn), pmul(w, pmul(q, psin(yn))));</div>
<div class="line"><a name="l01276"></a><span class="lineno"> 1276</span>&#160;    T y_gt_five = pmul(p, pmul(SQ2OPI, prsqrt(y)));</div>
<div class="line"><a name="l01277"></a><span class="lineno"> 1277</span>&#160;    <span class="keywordflow">return</span> pselect(pcmp_le(y, pset1&lt;T&gt;(5.0)), y_le_five, y_gt_five);</div>
<div class="line"><a name="l01278"></a><span class="lineno"> 1278</span>&#160;  }</div>
<div class="line"><a name="l01279"></a><span class="lineno"> 1279</span>&#160;};</div>
<div class="line"><a name="l01280"></a><span class="lineno"> 1280</span>&#160; </div>
<div class="line"><a name="l01281"></a><span class="lineno"> 1281</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l01282"></a><span class="lineno"> 1282</span>&#160;<span class="keyword">struct </span>bessel_j0_impl {</div>
<div class="line"><a name="l01283"></a><span class="lineno"> 1283</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l01284"></a><span class="lineno"> 1284</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T x) {</div>
<div class="line"><a name="l01285"></a><span class="lineno"> 1285</span>&#160;    <span class="keywordflow">return</span> generic_j0&lt;T&gt;::run(x);</div>
<div class="line"><a name="l01286"></a><span class="lineno"> 1286</span>&#160;  }</div>
<div class="line"><a name="l01287"></a><span class="lineno"> 1287</span>&#160;};</div>
<div class="line"><a name="l01288"></a><span class="lineno"> 1288</span>&#160; </div>
<div class="line"><a name="l01289"></a><span class="lineno"> 1289</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l01290"></a><span class="lineno"> 1290</span>&#160;<span class="keyword">struct </span>bessel_y0_retval {</div>
<div class="line"><a name="l01291"></a><span class="lineno"> 1291</span>&#160;  <span class="keyword">typedef</span> T type;</div>
<div class="line"><a name="l01292"></a><span class="lineno"> 1292</span>&#160;};</div>
<div class="line"><a name="l01293"></a><span class="lineno"> 1293</span>&#160; </div>
<div class="line"><a name="l01294"></a><span class="lineno"> 1294</span>&#160;template &lt;typename T, typename ScalarType = typename unpacket_traits&lt;T&gt;::type&gt;</div>
<div class="line"><a name="l01295"></a><span class="lineno"> 1295</span>&#160;<span class="keyword">struct </span>generic_y0 {</div>
<div class="line"><a name="l01296"></a><span class="lineno"> 1296</span>&#160;  EIGEN_STATIC_ASSERT((internal::is_same&lt;T, T&gt;::value == <span class="keyword">false</span>),</div>
<div class="line"><a name="l01297"></a><span class="lineno"> 1297</span>&#160;                      THIS_TYPE_IS_NOT_SUPPORTED)</div>
<div class="line"><a name="l01298"></a><span class="lineno"> 1298</span>&#160; </div>
<div class="line"><a name="l01299"></a><span class="lineno"> 1299</span>&#160;  EIGEN_DEVICE_FUNC <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp;) {</div>
<div class="line"><a name="l01300"></a><span class="lineno"> 1300</span>&#160;    <span class="keywordflow">return</span> ScalarType(0);</div>
<div class="line"><a name="l01301"></a><span class="lineno"> 1301</span>&#160;  }</div>
<div class="line"><a name="l01302"></a><span class="lineno"> 1302</span>&#160;};</div>
<div class="line"><a name="l01303"></a><span class="lineno"> 1303</span>&#160; </div>
<div class="line"><a name="l01304"></a><span class="lineno"> 1304</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l01305"></a><span class="lineno"> 1305</span>&#160;<span class="keyword">struct </span>generic_y0&lt;T, float&gt; {</div>
<div class="line"><a name="l01306"></a><span class="lineno"> 1306</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l01307"></a><span class="lineno"> 1307</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp; x) {</div>
<div class="line"><a name="l01308"></a><span class="lineno"> 1308</span>&#160;    <span class="comment">/* j0f.c</span></div>
<div class="line"><a name="l01309"></a><span class="lineno"> 1309</span>&#160;<span class="comment">     *  Bessel function of the second kind, order zero</span></div>
<div class="line"><a name="l01310"></a><span class="lineno"> 1310</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01311"></a><span class="lineno"> 1311</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01312"></a><span class="lineno"> 1312</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01313"></a><span class="lineno"> 1313</span>&#160;<span class="comment">     * SYNOPSIS:</span></div>
<div class="line"><a name="l01314"></a><span class="lineno"> 1314</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01315"></a><span class="lineno"> 1315</span>&#160;<span class="comment">     * float x, y, y0f();</span></div>
<div class="line"><a name="l01316"></a><span class="lineno"> 1316</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01317"></a><span class="lineno"> 1317</span>&#160;<span class="comment">     * y = y0f( x );</span></div>
<div class="line"><a name="l01318"></a><span class="lineno"> 1318</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01319"></a><span class="lineno"> 1319</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01320"></a><span class="lineno"> 1320</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01321"></a><span class="lineno"> 1321</span>&#160;<span class="comment">     * DESCRIPTION:</span></div>
<div class="line"><a name="l01322"></a><span class="lineno"> 1322</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01323"></a><span class="lineno"> 1323</span>&#160;<span class="comment">     * Returns Bessel function of the second kind, of order</span></div>
<div class="line"><a name="l01324"></a><span class="lineno"> 1324</span>&#160;<span class="comment">     * zero, of the argument.</span></div>
<div class="line"><a name="l01325"></a><span class="lineno"> 1325</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01326"></a><span class="lineno"> 1326</span>&#160;<span class="comment">     * The domain is divided into the intervals [0, 2] and</span></div>
<div class="line"><a name="l01327"></a><span class="lineno"> 1327</span>&#160;<span class="comment">     * (2, infinity). In the first interval a rational approximation</span></div>
<div class="line"><a name="l01328"></a><span class="lineno"> 1328</span>&#160;<span class="comment">     * R(x) is employed to compute</span></div>
<div class="line"><a name="l01329"></a><span class="lineno"> 1329</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01330"></a><span class="lineno"> 1330</span>&#160;<span class="comment">     *                  2         2         2</span></div>
<div class="line"><a name="l01331"></a><span class="lineno"> 1331</span>&#160;<span class="comment">     * y0(x)  =  (w - r  ) (w - r  ) (w - r  ) R(x)  +  2/pi ln(x) j0(x).</span></div>
<div class="line"><a name="l01332"></a><span class="lineno"> 1332</span>&#160;<span class="comment">     *                 1         2         3</span></div>
<div class="line"><a name="l01333"></a><span class="lineno"> 1333</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01334"></a><span class="lineno"> 1334</span>&#160;<span class="comment">     * Thus a call to j0() is required.  The three zeros are removed</span></div>
<div class="line"><a name="l01335"></a><span class="lineno"> 1335</span>&#160;<span class="comment">     * from R(x) to improve its numerical stability.</span></div>
<div class="line"><a name="l01336"></a><span class="lineno"> 1336</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01337"></a><span class="lineno"> 1337</span>&#160;<span class="comment">     * In the second interval, the modulus and phase are approximated</span></div>
<div class="line"><a name="l01338"></a><span class="lineno"> 1338</span>&#160;<span class="comment">     * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)</span></div>
<div class="line"><a name="l01339"></a><span class="lineno"> 1339</span>&#160;<span class="comment">     * and Phase(x) = x + 1/x S(1/x^2) - pi/4.  Then the function is</span></div>
<div class="line"><a name="l01340"></a><span class="lineno"> 1340</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01341"></a><span class="lineno"> 1341</span>&#160;<span class="comment">     *   y0(x) = Modulus(x) sin( Phase(x) ).</span></div>
<div class="line"><a name="l01342"></a><span class="lineno"> 1342</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01343"></a><span class="lineno"> 1343</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01344"></a><span class="lineno"> 1344</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01345"></a><span class="lineno"> 1345</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01346"></a><span class="lineno"> 1346</span>&#160;<span class="comment">     * ACCURACY:</span></div>
<div class="line"><a name="l01347"></a><span class="lineno"> 1347</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01348"></a><span class="lineno"> 1348</span>&#160;<span class="comment">     *  Absolute error, when y0(x) &lt; 1; else relative error:</span></div>
<div class="line"><a name="l01349"></a><span class="lineno"> 1349</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01350"></a><span class="lineno"> 1350</span>&#160;<span class="comment">     * arithmetic   domain     # trials      peak         rms</span></div>
<div class="line"><a name="l01351"></a><span class="lineno"> 1351</span>&#160;<span class="comment">     *    IEEE      0,  2       100000      2.4e-7      3.4e-8</span></div>
<div class="line"><a name="l01352"></a><span class="lineno"> 1352</span>&#160;<span class="comment">     *    IEEE      2, 32       100000      1.8e-7      5.3e-8</span></div>
<div class="line"><a name="l01353"></a><span class="lineno"> 1353</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01354"></a><span class="lineno"> 1354</span>&#160;<span class="comment">     */</span></div>
<div class="line"><a name="l01355"></a><span class="lineno"> 1355</span>&#160; </div>
<div class="line"><a name="l01356"></a><span class="lineno"> 1356</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> YP[] = {9.454583683980369E-008f, -9.413212653797057E-006f,</div>
<div class="line"><a name="l01357"></a><span class="lineno"> 1357</span>&#160;                        5.344486707214273E-004f, -1.584289289821316E-002f,</div>
<div class="line"><a name="l01358"></a><span class="lineno"> 1358</span>&#160;                        1.707584643733568E-001f};</div>
<div class="line"><a name="l01359"></a><span class="lineno"> 1359</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> MO[] = {-6.838999669318810E-002f, 1.864949361379502E-001f,</div>
<div class="line"><a name="l01360"></a><span class="lineno"> 1360</span>&#160;                        -2.145007480346739E-001f, 1.197549369473540E-001f,</div>
<div class="line"><a name="l01361"></a><span class="lineno"> 1361</span>&#160;                        -3.560281861530129E-003f, -4.969382655296620E-002f,</div>
<div class="line"><a name="l01362"></a><span class="lineno"> 1362</span>&#160;                        -3.355424622293709E-006f, 7.978845717621440E-001f};</div>
<div class="line"><a name="l01363"></a><span class="lineno"> 1363</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> PH[] = {3.242077816988247E+001f, -3.630592630518434E+001f,</div>
<div class="line"><a name="l01364"></a><span class="lineno"> 1364</span>&#160;                        1.756221482109099E+001f, -4.974978466280903E+000f,</div>
<div class="line"><a name="l01365"></a><span class="lineno"> 1365</span>&#160;                        1.001973420681837E+000f, -1.939906941791308E-001f,</div>
<div class="line"><a name="l01366"></a><span class="lineno"> 1366</span>&#160;                        6.490598792654666E-002f, -1.249992184872738E-001f};</div>
<div class="line"><a name="l01367"></a><span class="lineno"> 1367</span>&#160;    <span class="keyword">const</span> T YZ1 = pset1&lt;T&gt;(0.43221455686510834878f);</div>
<div class="line"><a name="l01368"></a><span class="lineno"> 1368</span>&#160;    <span class="keyword">const</span> T TWOOPI =  pset1&lt;T&gt;(0.636619772367581343075535f); <span class="comment">/* 2 / pi */</span></div>
<div class="line"><a name="l01369"></a><span class="lineno"> 1369</span>&#160;    <span class="keyword">const</span> T NEG_PIO4F = pset1&lt;T&gt;(-0.7853981633974483096f); <span class="comment">/* -pi / 4 */</span></div>
<div class="line"><a name="l01370"></a><span class="lineno"> 1370</span>&#160;    <span class="keyword">const</span> T NEG_MAXNUM = pset1&lt;T&gt;(-NumTraits&lt;float&gt;::infinity());</div>
<div class="line"><a name="l01371"></a><span class="lineno"> 1371</span>&#160;    T z = pmul(x, x);</div>
<div class="line"><a name="l01372"></a><span class="lineno"> 1372</span>&#160;    T x_le_two = pmul(TWOOPI, pmul(plog(x), generic_j0&lt;T, float&gt;::run(x)));</div>
<div class="line"><a name="l01373"></a><span class="lineno"> 1373</span>&#160;    x_le_two = pmadd(</div>
<div class="line"><a name="l01374"></a><span class="lineno"> 1374</span>&#160;        psub(z, YZ1), internal::ppolevl&lt;T, 4&gt;::run(z, YP), x_le_two);</div>
<div class="line"><a name="l01375"></a><span class="lineno"> 1375</span>&#160;    x_le_two = pselect(pcmp_le(x, pset1&lt;T&gt;(0.0)), NEG_MAXNUM, x_le_two);</div>
<div class="line"><a name="l01376"></a><span class="lineno"> 1376</span>&#160;    T q = pdiv(pset1&lt;T&gt;(1.0), x);</div>
<div class="line"><a name="l01377"></a><span class="lineno"> 1377</span>&#160;    T w = prsqrt(x);</div>
<div class="line"><a name="l01378"></a><span class="lineno"> 1378</span>&#160;    T p = pmul(w, internal::ppolevl&lt;T, 7&gt;::run(q, MO));</div>
<div class="line"><a name="l01379"></a><span class="lineno"> 1379</span>&#160;    T u = pmul(q, q);</div>
<div class="line"><a name="l01380"></a><span class="lineno"> 1380</span>&#160;    T xn = pmadd(q, internal::ppolevl&lt;T, 7&gt;::run(u, PH), NEG_PIO4F);</div>
<div class="line"><a name="l01381"></a><span class="lineno"> 1381</span>&#160;    T x_gt_two = pmul(p, psin(padd(xn, x)));</div>
<div class="line"><a name="l01382"></a><span class="lineno"> 1382</span>&#160;    <span class="keywordflow">return</span> pselect(pcmp_le(x, pset1&lt;T&gt;(2.0)), x_le_two, x_gt_two);</div>
<div class="line"><a name="l01383"></a><span class="lineno"> 1383</span>&#160;  }</div>
<div class="line"><a name="l01384"></a><span class="lineno"> 1384</span>&#160;};</div>
<div class="line"><a name="l01385"></a><span class="lineno"> 1385</span>&#160; </div>
<div class="line"><a name="l01386"></a><span class="lineno"> 1386</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l01387"></a><span class="lineno"> 1387</span>&#160;<span class="keyword">struct </span>generic_y0&lt;T, double&gt; {</div>
<div class="line"><a name="l01388"></a><span class="lineno"> 1388</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l01389"></a><span class="lineno"> 1389</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp; x) {</div>
<div class="line"><a name="l01390"></a><span class="lineno"> 1390</span>&#160;    <span class="comment">/*  j0.c</span></div>
<div class="line"><a name="l01391"></a><span class="lineno"> 1391</span>&#160;<span class="comment">     *  Bessel function of the second kind, order zero</span></div>
<div class="line"><a name="l01392"></a><span class="lineno"> 1392</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01393"></a><span class="lineno"> 1393</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01394"></a><span class="lineno"> 1394</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01395"></a><span class="lineno"> 1395</span>&#160;<span class="comment">     * SYNOPSIS:</span></div>
<div class="line"><a name="l01396"></a><span class="lineno"> 1396</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01397"></a><span class="lineno"> 1397</span>&#160;<span class="comment">     * double x, y, y0();</span></div>
<div class="line"><a name="l01398"></a><span class="lineno"> 1398</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01399"></a><span class="lineno"> 1399</span>&#160;<span class="comment">     * y = y0( x );</span></div>
<div class="line"><a name="l01400"></a><span class="lineno"> 1400</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01401"></a><span class="lineno"> 1401</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01402"></a><span class="lineno"> 1402</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01403"></a><span class="lineno"> 1403</span>&#160;<span class="comment">     * DESCRIPTION:</span></div>
<div class="line"><a name="l01404"></a><span class="lineno"> 1404</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01405"></a><span class="lineno"> 1405</span>&#160;<span class="comment">     * Returns Bessel function of the second kind, of order</span></div>
<div class="line"><a name="l01406"></a><span class="lineno"> 1406</span>&#160;<span class="comment">     * zero, of the argument.</span></div>
<div class="line"><a name="l01407"></a><span class="lineno"> 1407</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01408"></a><span class="lineno"> 1408</span>&#160;<span class="comment">     * The domain is divided into the intervals [0, 5] and</span></div>
<div class="line"><a name="l01409"></a><span class="lineno"> 1409</span>&#160;<span class="comment">     * (5, infinity). In the first interval a rational approximation</span></div>
<div class="line"><a name="l01410"></a><span class="lineno"> 1410</span>&#160;<span class="comment">     * R(x) is employed to compute</span></div>
<div class="line"><a name="l01411"></a><span class="lineno"> 1411</span>&#160;<span class="comment">     *   y0(x)  = R(x)  +   2 * log(x) * j0(x) / PI.</span></div>
<div class="line"><a name="l01412"></a><span class="lineno"> 1412</span>&#160;<span class="comment">     * Thus a call to j0() is required.</span></div>
<div class="line"><a name="l01413"></a><span class="lineno"> 1413</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01414"></a><span class="lineno"> 1414</span>&#160;<span class="comment">     * In the second interval, the Hankel asymptotic expansion</span></div>
<div class="line"><a name="l01415"></a><span class="lineno"> 1415</span>&#160;<span class="comment">     * is employed with two rational functions of degree 6/6</span></div>
<div class="line"><a name="l01416"></a><span class="lineno"> 1416</span>&#160;<span class="comment">     * and 7/7.</span></div>
<div class="line"><a name="l01417"></a><span class="lineno"> 1417</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01418"></a><span class="lineno"> 1418</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01419"></a><span class="lineno"> 1419</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01420"></a><span class="lineno"> 1420</span>&#160;<span class="comment">     * ACCURACY:</span></div>
<div class="line"><a name="l01421"></a><span class="lineno"> 1421</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01422"></a><span class="lineno"> 1422</span>&#160;<span class="comment">     *  Absolute error, when y0(x) &lt; 1; else relative error:</span></div>
<div class="line"><a name="l01423"></a><span class="lineno"> 1423</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01424"></a><span class="lineno"> 1424</span>&#160;<span class="comment">     * arithmetic   domain     # trials      peak         rms</span></div>
<div class="line"><a name="l01425"></a><span class="lineno"> 1425</span>&#160;<span class="comment">     *    DEC       0, 30        9400       7.0e-17     7.9e-18</span></div>
<div class="line"><a name="l01426"></a><span class="lineno"> 1426</span>&#160;<span class="comment">     *    IEEE      0, 30       30000       1.3e-15     1.6e-16</span></div>
<div class="line"><a name="l01427"></a><span class="lineno"> 1427</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01428"></a><span class="lineno"> 1428</span>&#160;<span class="comment">     */</span></div>
<div class="line"><a name="l01429"></a><span class="lineno"> 1429</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> PP[] = {7.96936729297347051624E-4, 8.28352392107440799803E-2,</div>
<div class="line"><a name="l01430"></a><span class="lineno"> 1430</span>&#160;                        1.23953371646414299388E0, 5.44725003058768775090E0,</div>
<div class="line"><a name="l01431"></a><span class="lineno"> 1431</span>&#160;                        8.74716500199817011941E0, 5.30324038235394892183E0,</div>
<div class="line"><a name="l01432"></a><span class="lineno"> 1432</span>&#160;                        9.99999999999999997821E-1};</div>
<div class="line"><a name="l01433"></a><span class="lineno"> 1433</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> PQ[] = {9.24408810558863637013E-4, 8.56288474354474431428E-2,</div>
<div class="line"><a name="l01434"></a><span class="lineno"> 1434</span>&#160;                         1.25352743901058953537E0, 5.47097740330417105182E0,</div>
<div class="line"><a name="l01435"></a><span class="lineno"> 1435</span>&#160;                         8.76190883237069594232E0, 5.30605288235394617618E0,</div>
<div class="line"><a name="l01436"></a><span class="lineno"> 1436</span>&#160;                         1.00000000000000000218E0};</div>
<div class="line"><a name="l01437"></a><span class="lineno"> 1437</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> QP[] = {-1.13663838898469149931E-2, -1.28252718670509318512E0,</div>
<div class="line"><a name="l01438"></a><span class="lineno"> 1438</span>&#160;                         -1.95539544257735972385E1, -9.32060152123768231369E1,</div>
<div class="line"><a name="l01439"></a><span class="lineno"> 1439</span>&#160;                         -1.77681167980488050595E2, -1.47077505154951170175E2,</div>
<div class="line"><a name="l01440"></a><span class="lineno"> 1440</span>&#160;                         -5.14105326766599330220E1, -6.05014350600728481186E0};</div>
<div class="line"><a name="l01441"></a><span class="lineno"> 1441</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> QQ[] = {1.00000000000000000000E0, 6.43178256118178023184E1,</div>
<div class="line"><a name="l01442"></a><span class="lineno"> 1442</span>&#160;                         8.56430025976980587198E2, 3.88240183605401609683E3,</div>
<div class="line"><a name="l01443"></a><span class="lineno"> 1443</span>&#160;                         7.24046774195652478189E3, 5.93072701187316984827E3,</div>
<div class="line"><a name="l01444"></a><span class="lineno"> 1444</span>&#160;                         2.06209331660327847417E3, 2.42005740240291393179E2};</div>
<div class="line"><a name="l01445"></a><span class="lineno"> 1445</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> YP[] = {1.55924367855235737965E4, -1.46639295903971606143E7,</div>
<div class="line"><a name="l01446"></a><span class="lineno"> 1446</span>&#160;                         5.43526477051876500413E9, -9.82136065717911466409E11,</div>
<div class="line"><a name="l01447"></a><span class="lineno"> 1447</span>&#160;                         8.75906394395366999549E13, -3.46628303384729719441E15,</div>
<div class="line"><a name="l01448"></a><span class="lineno"> 1448</span>&#160;                         4.42733268572569800351E16, -1.84950800436986690637E16};</div>
<div class="line"><a name="l01449"></a><span class="lineno"> 1449</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> YQ[] = {1.00000000000000000000E0,  1.04128353664259848412E3,</div>
<div class="line"><a name="l01450"></a><span class="lineno"> 1450</span>&#160;                         6.26107330137134956842E5, 2.68919633393814121987E8,</div>
<div class="line"><a name="l01451"></a><span class="lineno"> 1451</span>&#160;                         8.64002487103935000337E10, 2.02979612750105546709E13,</div>
<div class="line"><a name="l01452"></a><span class="lineno"> 1452</span>&#160;                         3.17157752842975028269E15, 2.50596256172653059228E17};</div>
<div class="line"><a name="l01453"></a><span class="lineno"> 1453</span>&#160;    <span class="keyword">const</span> T SQ2OPI = pset1&lt;T&gt;(7.9788456080286535587989E-1); <span class="comment">/* sqrt(2 / pi) */</span></div>
<div class="line"><a name="l01454"></a><span class="lineno"> 1454</span>&#160;    <span class="keyword">const</span> T TWOOPI =  pset1&lt;T&gt;(0.636619772367581343075535); <span class="comment">/* 2 / pi */</span></div>
<div class="line"><a name="l01455"></a><span class="lineno"> 1455</span>&#160;    <span class="keyword">const</span> T NEG_PIO4 = pset1&lt;T&gt;(-0.7853981633974483096); <span class="comment">/* -pi / 4 */</span></div>
<div class="line"><a name="l01456"></a><span class="lineno"> 1456</span>&#160;    <span class="keyword">const</span> T NEG_MAXNUM = pset1&lt;T&gt;(-NumTraits&lt;double&gt;::infinity());</div>
<div class="line"><a name="l01457"></a><span class="lineno"> 1457</span>&#160; </div>
<div class="line"><a name="l01458"></a><span class="lineno"> 1458</span>&#160;    T z = pmul(x, x);</div>
<div class="line"><a name="l01459"></a><span class="lineno"> 1459</span>&#160;    T x_le_five = pdiv(internal::ppolevl&lt;T, 7&gt;::run(z, YP),</div>
<div class="line"><a name="l01460"></a><span class="lineno"> 1460</span>&#160;                       internal::ppolevl&lt;T, 7&gt;::run(z, YQ));</div>
<div class="line"><a name="l01461"></a><span class="lineno"> 1461</span>&#160;    x_le_five = pmadd(</div>
<div class="line"><a name="l01462"></a><span class="lineno"> 1462</span>&#160;        pmul(TWOOPI, plog(x)), generic_j0&lt;T, double&gt;::run(x), x_le_five);</div>
<div class="line"><a name="l01463"></a><span class="lineno"> 1463</span>&#160;    x_le_five = pselect(pcmp_le(x, pset1&lt;T&gt;(0.0)), NEG_MAXNUM, x_le_five);</div>
<div class="line"><a name="l01464"></a><span class="lineno"> 1464</span>&#160;    T s = pdiv(pset1&lt;T&gt;(25.0), z);</div>
<div class="line"><a name="l01465"></a><span class="lineno"> 1465</span>&#160;    T p = pdiv(</div>
<div class="line"><a name="l01466"></a><span class="lineno"> 1466</span>&#160;        internal::ppolevl&lt;T, 6&gt;::run(s, PP),</div>
<div class="line"><a name="l01467"></a><span class="lineno"> 1467</span>&#160;        internal::ppolevl&lt;T, 6&gt;::run(s, PQ));</div>
<div class="line"><a name="l01468"></a><span class="lineno"> 1468</span>&#160;    T q = pdiv(</div>
<div class="line"><a name="l01469"></a><span class="lineno"> 1469</span>&#160;        internal::ppolevl&lt;T, 7&gt;::run(s, QP),</div>
<div class="line"><a name="l01470"></a><span class="lineno"> 1470</span>&#160;        internal::ppolevl&lt;T, 7&gt;::run(s, QQ));</div>
<div class="line"><a name="l01471"></a><span class="lineno"> 1471</span>&#160;    T xn = padd(x, NEG_PIO4);</div>
<div class="line"><a name="l01472"></a><span class="lineno"> 1472</span>&#160;    T w = pdiv(pset1&lt;T&gt;(5.0), x);</div>
<div class="line"><a name="l01473"></a><span class="lineno"> 1473</span>&#160;    p = pmadd(p, psin(xn), pmul(w, pmul(q, pcos(xn))));</div>
<div class="line"><a name="l01474"></a><span class="lineno"> 1474</span>&#160;    T x_gt_five = pmul(p, pmul(SQ2OPI, prsqrt(x)));</div>
<div class="line"><a name="l01475"></a><span class="lineno"> 1475</span>&#160;    <span class="keywordflow">return</span> pselect(pcmp_le(x, pset1&lt;T&gt;(5.0)), x_le_five, x_gt_five);</div>
<div class="line"><a name="l01476"></a><span class="lineno"> 1476</span>&#160;  }</div>
<div class="line"><a name="l01477"></a><span class="lineno"> 1477</span>&#160;};</div>
<div class="line"><a name="l01478"></a><span class="lineno"> 1478</span>&#160; </div>
<div class="line"><a name="l01479"></a><span class="lineno"> 1479</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l01480"></a><span class="lineno"> 1480</span>&#160;<span class="keyword">struct </span>bessel_y0_impl {</div>
<div class="line"><a name="l01481"></a><span class="lineno"> 1481</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l01482"></a><span class="lineno"> 1482</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T x) {</div>
<div class="line"><a name="l01483"></a><span class="lineno"> 1483</span>&#160;    <span class="keywordflow">return</span> generic_y0&lt;T&gt;::run(x);</div>
<div class="line"><a name="l01484"></a><span class="lineno"> 1484</span>&#160;  }</div>
<div class="line"><a name="l01485"></a><span class="lineno"> 1485</span>&#160;};</div>
<div class="line"><a name="l01486"></a><span class="lineno"> 1486</span>&#160; </div>
<div class="line"><a name="l01487"></a><span class="lineno"> 1487</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l01488"></a><span class="lineno"> 1488</span>&#160;<span class="keyword">struct </span>bessel_j1_retval {</div>
<div class="line"><a name="l01489"></a><span class="lineno"> 1489</span>&#160;  <span class="keyword">typedef</span> T type;</div>
<div class="line"><a name="l01490"></a><span class="lineno"> 1490</span>&#160;};</div>
<div class="line"><a name="l01491"></a><span class="lineno"> 1491</span>&#160; </div>
<div class="line"><a name="l01492"></a><span class="lineno"> 1492</span>&#160;template &lt;typename T, typename ScalarType = typename unpacket_traits&lt;T&gt;::type&gt;</div>
<div class="line"><a name="l01493"></a><span class="lineno"> 1493</span>&#160;<span class="keyword">struct </span>generic_j1 {</div>
<div class="line"><a name="l01494"></a><span class="lineno"> 1494</span>&#160;  EIGEN_STATIC_ASSERT((internal::is_same&lt;T, T&gt;::value == <span class="keyword">false</span>),</div>
<div class="line"><a name="l01495"></a><span class="lineno"> 1495</span>&#160;                      THIS_TYPE_IS_NOT_SUPPORTED)</div>
<div class="line"><a name="l01496"></a><span class="lineno"> 1496</span>&#160; </div>
<div class="line"><a name="l01497"></a><span class="lineno"> 1497</span>&#160;  EIGEN_DEVICE_FUNC <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp;) {</div>
<div class="line"><a name="l01498"></a><span class="lineno"> 1498</span>&#160;    <span class="keywordflow">return</span> ScalarType(0);</div>
<div class="line"><a name="l01499"></a><span class="lineno"> 1499</span>&#160;  }</div>
<div class="line"><a name="l01500"></a><span class="lineno"> 1500</span>&#160;};</div>
<div class="line"><a name="l01501"></a><span class="lineno"> 1501</span>&#160; </div>
<div class="line"><a name="l01502"></a><span class="lineno"> 1502</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l01503"></a><span class="lineno"> 1503</span>&#160;<span class="keyword">struct </span>generic_j1&lt;T, float&gt; {</div>
<div class="line"><a name="l01504"></a><span class="lineno"> 1504</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l01505"></a><span class="lineno"> 1505</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp; x) {</div>
<div class="line"><a name="l01506"></a><span class="lineno"> 1506</span>&#160;    <span class="comment">/* j1f.c</span></div>
<div class="line"><a name="l01507"></a><span class="lineno"> 1507</span>&#160;<span class="comment">     *  Bessel function of order one</span></div>
<div class="line"><a name="l01508"></a><span class="lineno"> 1508</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01509"></a><span class="lineno"> 1509</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01510"></a><span class="lineno"> 1510</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01511"></a><span class="lineno"> 1511</span>&#160;<span class="comment">     * SYNOPSIS:</span></div>
<div class="line"><a name="l01512"></a><span class="lineno"> 1512</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01513"></a><span class="lineno"> 1513</span>&#160;<span class="comment">     * float x, y, j1f();</span></div>
<div class="line"><a name="l01514"></a><span class="lineno"> 1514</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01515"></a><span class="lineno"> 1515</span>&#160;<span class="comment">     * y = j1f( x );</span></div>
<div class="line"><a name="l01516"></a><span class="lineno"> 1516</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01517"></a><span class="lineno"> 1517</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01518"></a><span class="lineno"> 1518</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01519"></a><span class="lineno"> 1519</span>&#160;<span class="comment">     * DESCRIPTION:</span></div>
<div class="line"><a name="l01520"></a><span class="lineno"> 1520</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01521"></a><span class="lineno"> 1521</span>&#160;<span class="comment">     * Returns Bessel function of order one of the argument.</span></div>
<div class="line"><a name="l01522"></a><span class="lineno"> 1522</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01523"></a><span class="lineno"> 1523</span>&#160;<span class="comment">     * The domain is divided into the intervals [0, 2] and</span></div>
<div class="line"><a name="l01524"></a><span class="lineno"> 1524</span>&#160;<span class="comment">     * (2, infinity). In the first interval a polynomial approximation</span></div>
<div class="line"><a name="l01525"></a><span class="lineno"> 1525</span>&#160;<span class="comment">     *        2</span></div>
<div class="line"><a name="l01526"></a><span class="lineno"> 1526</span>&#160;<span class="comment">     * (w - r  ) x P(w)</span></div>
<div class="line"><a name="l01527"></a><span class="lineno"> 1527</span>&#160;<span class="comment">     *       1</span></div>
<div class="line"><a name="l01528"></a><span class="lineno"> 1528</span>&#160;<span class="comment">     *                     2</span></div>
<div class="line"><a name="l01529"></a><span class="lineno"> 1529</span>&#160;<span class="comment">     * is used, where w = x  and r is the first zero of the function.</span></div>
<div class="line"><a name="l01530"></a><span class="lineno"> 1530</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01531"></a><span class="lineno"> 1531</span>&#160;<span class="comment">     * In the second interval, the modulus and phase are approximated</span></div>
<div class="line"><a name="l01532"></a><span class="lineno"> 1532</span>&#160;<span class="comment">     * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)</span></div>
<div class="line"><a name="l01533"></a><span class="lineno"> 1533</span>&#160;<span class="comment">     * and Phase(x) = x + 1/x R(1/x^2) - 3pi/4.  The function is</span></div>
<div class="line"><a name="l01534"></a><span class="lineno"> 1534</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01535"></a><span class="lineno"> 1535</span>&#160;<span class="comment">     *   j0(x) = Modulus(x) cos( Phase(x) ).</span></div>
<div class="line"><a name="l01536"></a><span class="lineno"> 1536</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01537"></a><span class="lineno"> 1537</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01538"></a><span class="lineno"> 1538</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01539"></a><span class="lineno"> 1539</span>&#160;<span class="comment">     * ACCURACY:</span></div>
<div class="line"><a name="l01540"></a><span class="lineno"> 1540</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01541"></a><span class="lineno"> 1541</span>&#160;<span class="comment">     *                      Absolute error:</span></div>
<div class="line"><a name="l01542"></a><span class="lineno"> 1542</span>&#160;<span class="comment">     * arithmetic   domain      # trials      peak       rms</span></div>
<div class="line"><a name="l01543"></a><span class="lineno"> 1543</span>&#160;<span class="comment">     *    IEEE      0,  2       100000       1.2e-7     2.5e-8</span></div>
<div class="line"><a name="l01544"></a><span class="lineno"> 1544</span>&#160;<span class="comment">     *    IEEE      2, 32       100000       2.0e-7     5.3e-8</span></div>
<div class="line"><a name="l01545"></a><span class="lineno"> 1545</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01546"></a><span class="lineno"> 1546</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01547"></a><span class="lineno"> 1547</span>&#160;<span class="comment">     */</span></div>
<div class="line"><a name="l01548"></a><span class="lineno"> 1548</span>&#160; </div>
<div class="line"><a name="l01549"></a><span class="lineno"> 1549</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> JP[] = {-4.878788132172128E-009f, 6.009061827883699E-007f,</div>
<div class="line"><a name="l01550"></a><span class="lineno"> 1550</span>&#160;                        -4.541343896997497E-005f, 1.937383947804541E-003f,</div>
<div class="line"><a name="l01551"></a><span class="lineno"> 1551</span>&#160;                        -3.405537384615824E-002f};</div>
<div class="line"><a name="l01552"></a><span class="lineno"> 1552</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> MO1[] = {6.913942741265801E-002f, -2.284801500053359E-001f,</div>
<div class="line"><a name="l01553"></a><span class="lineno"> 1553</span>&#160;                        3.138238455499697E-001f, -2.102302420403875E-001f,</div>
<div class="line"><a name="l01554"></a><span class="lineno"> 1554</span>&#160;                        5.435364690523026E-003f, 1.493389585089498E-001f,</div>
<div class="line"><a name="l01555"></a><span class="lineno"> 1555</span>&#160;                        4.976029650847191E-006f, 7.978845453073848E-001f};</div>
<div class="line"><a name="l01556"></a><span class="lineno"> 1556</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> PH1[] = {-4.497014141919556E+001f, 5.073465654089319E+001f,</div>
<div class="line"><a name="l01557"></a><span class="lineno"> 1557</span>&#160;                        -2.485774108720340E+001f, 7.222973196770240E+000f,</div>
<div class="line"><a name="l01558"></a><span class="lineno"> 1558</span>&#160;                        -1.544842782180211E+000f, 3.503787691653334E-001f,</div>
<div class="line"><a name="l01559"></a><span class="lineno"> 1559</span>&#160;                        -1.637986776941202E-001f, 3.749989509080821E-001f};</div>
<div class="line"><a name="l01560"></a><span class="lineno"> 1560</span>&#160;    <span class="keyword">const</span> T Z1 = pset1&lt;T&gt;(1.46819706421238932572E1f);</div>
<div class="line"><a name="l01561"></a><span class="lineno"> 1561</span>&#160;    <span class="keyword">const</span> T NEG_THPIO4F = pset1&lt;T&gt;(-2.35619449019234492885f);    <span class="comment">/* -3*pi/4 */</span></div>
<div class="line"><a name="l01562"></a><span class="lineno"> 1562</span>&#160; </div>
<div class="line"><a name="l01563"></a><span class="lineno"> 1563</span>&#160;    T y = pabs(x);</div>
<div class="line"><a name="l01564"></a><span class="lineno"> 1564</span>&#160;    T z = pmul(y, y);</div>
<div class="line"><a name="l01565"></a><span class="lineno"> 1565</span>&#160;    T y_le_two = pmul(</div>
<div class="line"><a name="l01566"></a><span class="lineno"> 1566</span>&#160;        psub(z, Z1),</div>
<div class="line"><a name="l01567"></a><span class="lineno"> 1567</span>&#160;        pmul(x, internal::ppolevl&lt;T, 4&gt;::run(z, JP)));</div>
<div class="line"><a name="l01568"></a><span class="lineno"> 1568</span>&#160;    T q = pdiv(pset1&lt;T&gt;(1.0f), y);</div>
<div class="line"><a name="l01569"></a><span class="lineno"> 1569</span>&#160;    T w = prsqrt(y);</div>
<div class="line"><a name="l01570"></a><span class="lineno"> 1570</span>&#160;    T p = pmul(w, internal::ppolevl&lt;T, 7&gt;::run(q, MO1));</div>
<div class="line"><a name="l01571"></a><span class="lineno"> 1571</span>&#160;    w = pmul(q, q);</div>
<div class="line"><a name="l01572"></a><span class="lineno"> 1572</span>&#160;    T yn = pmadd(q, internal::ppolevl&lt;T, 7&gt;::run(w, PH1), NEG_THPIO4F);</div>
<div class="line"><a name="l01573"></a><span class="lineno"> 1573</span>&#160;    T y_gt_two = pmul(p, pcos(padd(yn, y)));</div>
<div class="line"><a name="l01574"></a><span class="lineno"> 1574</span>&#160;    <span class="comment">// j1 is an odd function. This implementation differs from cephes to</span></div>
<div class="line"><a name="l01575"></a><span class="lineno"> 1575</span>&#160;    <span class="comment">// take this fact in to account. Cephes returns -j1(x) for y &gt; 2 range.</span></div>
<div class="line"><a name="l01576"></a><span class="lineno"> 1576</span>&#160;    y_gt_two = pselect(</div>
<div class="line"><a name="l01577"></a><span class="lineno"> 1577</span>&#160;        pcmp_lt(x, pset1&lt;T&gt;(0.0f)), pnegate(y_gt_two), y_gt_two);</div>
<div class="line"><a name="l01578"></a><span class="lineno"> 1578</span>&#160;    <span class="keywordflow">return</span> pselect(pcmp_le(y, pset1&lt;T&gt;(2.0f)), y_le_two, y_gt_two);</div>
<div class="line"><a name="l01579"></a><span class="lineno"> 1579</span>&#160;  }</div>
<div class="line"><a name="l01580"></a><span class="lineno"> 1580</span>&#160;};</div>
<div class="line"><a name="l01581"></a><span class="lineno"> 1581</span>&#160; </div>
<div class="line"><a name="l01582"></a><span class="lineno"> 1582</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l01583"></a><span class="lineno"> 1583</span>&#160;<span class="keyword">struct </span>generic_j1&lt;T, double&gt; {</div>
<div class="line"><a name="l01584"></a><span class="lineno"> 1584</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l01585"></a><span class="lineno"> 1585</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp; x) {</div>
<div class="line"><a name="l01586"></a><span class="lineno"> 1586</span>&#160;    <span class="comment">/*  j1.c</span></div>
<div class="line"><a name="l01587"></a><span class="lineno"> 1587</span>&#160;<span class="comment">     *  Bessel function of order one</span></div>
<div class="line"><a name="l01588"></a><span class="lineno"> 1588</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01589"></a><span class="lineno"> 1589</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01590"></a><span class="lineno"> 1590</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01591"></a><span class="lineno"> 1591</span>&#160;<span class="comment">     * SYNOPSIS:</span></div>
<div class="line"><a name="l01592"></a><span class="lineno"> 1592</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01593"></a><span class="lineno"> 1593</span>&#160;<span class="comment">     * double x, y, j1();</span></div>
<div class="line"><a name="l01594"></a><span class="lineno"> 1594</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01595"></a><span class="lineno"> 1595</span>&#160;<span class="comment">     * y = j1( x );</span></div>
<div class="line"><a name="l01596"></a><span class="lineno"> 1596</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01597"></a><span class="lineno"> 1597</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01598"></a><span class="lineno"> 1598</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01599"></a><span class="lineno"> 1599</span>&#160;<span class="comment">     * DESCRIPTION:</span></div>
<div class="line"><a name="l01600"></a><span class="lineno"> 1600</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01601"></a><span class="lineno"> 1601</span>&#160;<span class="comment">     * Returns Bessel function of order one of the argument.</span></div>
<div class="line"><a name="l01602"></a><span class="lineno"> 1602</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01603"></a><span class="lineno"> 1603</span>&#160;<span class="comment">     * The domain is divided into the intervals [0, 8] and</span></div>
<div class="line"><a name="l01604"></a><span class="lineno"> 1604</span>&#160;<span class="comment">     * (8, infinity). In the first interval a 24 term Chebyshev</span></div>
<div class="line"><a name="l01605"></a><span class="lineno"> 1605</span>&#160;<span class="comment">     * expansion is used. In the second, the asymptotic</span></div>
<div class="line"><a name="l01606"></a><span class="lineno"> 1606</span>&#160;<span class="comment">     * trigonometric representation is employed using two</span></div>
<div class="line"><a name="l01607"></a><span class="lineno"> 1607</span>&#160;<span class="comment">     * rational functions of degree 5/5.</span></div>
<div class="line"><a name="l01608"></a><span class="lineno"> 1608</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01609"></a><span class="lineno"> 1609</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01610"></a><span class="lineno"> 1610</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01611"></a><span class="lineno"> 1611</span>&#160;<span class="comment">     * ACCURACY:</span></div>
<div class="line"><a name="l01612"></a><span class="lineno"> 1612</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01613"></a><span class="lineno"> 1613</span>&#160;<span class="comment">     *                      Absolute error:</span></div>
<div class="line"><a name="l01614"></a><span class="lineno"> 1614</span>&#160;<span class="comment">     * arithmetic   domain      # trials      peak         rms</span></div>
<div class="line"><a name="l01615"></a><span class="lineno"> 1615</span>&#160;<span class="comment">     *    DEC       0, 30       10000       4.0e-17     1.1e-17</span></div>
<div class="line"><a name="l01616"></a><span class="lineno"> 1616</span>&#160;<span class="comment">     *    IEEE      0, 30       30000       2.6e-16     1.1e-16</span></div>
<div class="line"><a name="l01617"></a><span class="lineno"> 1617</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01618"></a><span class="lineno"> 1618</span>&#160;<span class="comment">     */</span></div>
<div class="line"><a name="l01619"></a><span class="lineno"> 1619</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> PP[] = {7.62125616208173112003E-4, 7.31397056940917570436E-2,</div>
<div class="line"><a name="l01620"></a><span class="lineno"> 1620</span>&#160;                         1.12719608129684925192E0, 5.11207951146807644818E0,</div>
<div class="line"><a name="l01621"></a><span class="lineno"> 1621</span>&#160;                         8.42404590141772420927E0, 5.21451598682361504063E0,</div>
<div class="line"><a name="l01622"></a><span class="lineno"> 1622</span>&#160;                         1.00000000000000000254E0};</div>
<div class="line"><a name="l01623"></a><span class="lineno"> 1623</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> PQ[] = {5.71323128072548699714E-4, 6.88455908754495404082E-2,</div>
<div class="line"><a name="l01624"></a><span class="lineno"> 1624</span>&#160;                         1.10514232634061696926E0, 5.07386386128601488557E0,</div>
<div class="line"><a name="l01625"></a><span class="lineno"> 1625</span>&#160;                         8.39985554327604159757E0, 5.20982848682361821619E0,</div>
<div class="line"><a name="l01626"></a><span class="lineno"> 1626</span>&#160;                         9.99999999999999997461E-1};</div>
<div class="line"><a name="l01627"></a><span class="lineno"> 1627</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> QP[] = {5.10862594750176621635E-2, 4.98213872951233449420E0,</div>
<div class="line"><a name="l01628"></a><span class="lineno"> 1628</span>&#160;                         7.58238284132545283818E1, 3.66779609360150777800E2,</div>
<div class="line"><a name="l01629"></a><span class="lineno"> 1629</span>&#160;                         7.10856304998926107277E2, 5.97489612400613639965E2,</div>
<div class="line"><a name="l01630"></a><span class="lineno"> 1630</span>&#160;                         2.11688757100572135698E2, 2.52070205858023719784E1};</div>
<div class="line"><a name="l01631"></a><span class="lineno"> 1631</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> QQ[] = {1.00000000000000000000E0, 7.42373277035675149943E1,</div>
<div class="line"><a name="l01632"></a><span class="lineno"> 1632</span>&#160;                         1.05644886038262816351E3, 4.98641058337653607651E3,</div>
<div class="line"><a name="l01633"></a><span class="lineno"> 1633</span>&#160;                         9.56231892404756170795E3, 7.99704160447350683650E3,</div>
<div class="line"><a name="l01634"></a><span class="lineno"> 1634</span>&#160;                         2.82619278517639096600E3, 3.36093607810698293419E2};</div>
<div class="line"><a name="l01635"></a><span class="lineno"> 1635</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> RP[] = {-8.99971225705559398224E8, 4.52228297998194034323E11,</div>
<div class="line"><a name="l01636"></a><span class="lineno"> 1636</span>&#160;                         -7.27494245221818276015E13, 3.68295732863852883286E15};</div>
<div class="line"><a name="l01637"></a><span class="lineno"> 1637</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> RQ[] = {1.00000000000000000000E0, 6.20836478118054335476E2,</div>
<div class="line"><a name="l01638"></a><span class="lineno"> 1638</span>&#160;                         2.56987256757748830383E5, 8.35146791431949253037E7,</div>
<div class="line"><a name="l01639"></a><span class="lineno"> 1639</span>&#160;                         2.21511595479792499675E10, 4.74914122079991414898E12,</div>
<div class="line"><a name="l01640"></a><span class="lineno"> 1640</span>&#160;                         7.84369607876235854894E14, 8.95222336184627338078E16,</div>
<div class="line"><a name="l01641"></a><span class="lineno"> 1641</span>&#160;                         5.32278620332680085395E18};</div>
<div class="line"><a name="l01642"></a><span class="lineno"> 1642</span>&#160;    <span class="keyword">const</span> T Z1 = pset1&lt;T&gt;(1.46819706421238932572E1);</div>
<div class="line"><a name="l01643"></a><span class="lineno"> 1643</span>&#160;    <span class="keyword">const</span> T Z2 = pset1&lt;T&gt;(4.92184563216946036703E1);</div>
<div class="line"><a name="l01644"></a><span class="lineno"> 1644</span>&#160;    <span class="keyword">const</span> T NEG_THPIO4 = pset1&lt;T&gt;(-2.35619449019234492885);    <span class="comment">/* -3*pi/4 */</span></div>
<div class="line"><a name="l01645"></a><span class="lineno"> 1645</span>&#160;    <span class="keyword">const</span> T SQ2OPI = pset1&lt;T&gt;(7.9788456080286535587989E-1); <span class="comment">/* sqrt(2 / pi) */</span></div>
<div class="line"><a name="l01646"></a><span class="lineno"> 1646</span>&#160;    T y = pabs(x);</div>
<div class="line"><a name="l01647"></a><span class="lineno"> 1647</span>&#160;    T z = pmul(y, y);</div>
<div class="line"><a name="l01648"></a><span class="lineno"> 1648</span>&#160;    T y_le_five = pdiv(internal::ppolevl&lt;T, 3&gt;::run(z, RP),</div>
<div class="line"><a name="l01649"></a><span class="lineno"> 1649</span>&#160;                       internal::ppolevl&lt;T, 8&gt;::run(z, RQ));</div>
<div class="line"><a name="l01650"></a><span class="lineno"> 1650</span>&#160;    y_le_five = pmul(pmul(pmul(y_le_five, x), psub(z, Z1)), psub(z, Z2));</div>
<div class="line"><a name="l01651"></a><span class="lineno"> 1651</span>&#160;    T s = pdiv(pset1&lt;T&gt;(25.0), z);</div>
<div class="line"><a name="l01652"></a><span class="lineno"> 1652</span>&#160;    T p = pdiv(</div>
<div class="line"><a name="l01653"></a><span class="lineno"> 1653</span>&#160;        internal::ppolevl&lt;T, 6&gt;::run(s, PP),</div>
<div class="line"><a name="l01654"></a><span class="lineno"> 1654</span>&#160;        internal::ppolevl&lt;T, 6&gt;::run(s, PQ));</div>
<div class="line"><a name="l01655"></a><span class="lineno"> 1655</span>&#160;    T q = pdiv(</div>
<div class="line"><a name="l01656"></a><span class="lineno"> 1656</span>&#160;        internal::ppolevl&lt;T, 7&gt;::run(s, QP),</div>
<div class="line"><a name="l01657"></a><span class="lineno"> 1657</span>&#160;        internal::ppolevl&lt;T, 7&gt;::run(s, QQ));</div>
<div class="line"><a name="l01658"></a><span class="lineno"> 1658</span>&#160;    T yn = padd(y, NEG_THPIO4);</div>
<div class="line"><a name="l01659"></a><span class="lineno"> 1659</span>&#160;    T w = pdiv(pset1&lt;T&gt;(-5.0), y);</div>
<div class="line"><a name="l01660"></a><span class="lineno"> 1660</span>&#160;    p = pmadd(p, pcos(yn), pmul(w, pmul(q, psin(yn))));</div>
<div class="line"><a name="l01661"></a><span class="lineno"> 1661</span>&#160;    T y_gt_five = pmul(p, pmul(SQ2OPI, prsqrt(y)));</div>
<div class="line"><a name="l01662"></a><span class="lineno"> 1662</span>&#160;    <span class="comment">// j1 is an odd function. This implementation differs from cephes to</span></div>
<div class="line"><a name="l01663"></a><span class="lineno"> 1663</span>&#160;    <span class="comment">// take this fact in to account. Cephes returns -j1(x) for y &gt; 5 range.</span></div>
<div class="line"><a name="l01664"></a><span class="lineno"> 1664</span>&#160;    y_gt_five = pselect(</div>
<div class="line"><a name="l01665"></a><span class="lineno"> 1665</span>&#160;        pcmp_lt(x, pset1&lt;T&gt;(0.0)), pnegate(y_gt_five), y_gt_five);</div>
<div class="line"><a name="l01666"></a><span class="lineno"> 1666</span>&#160;    <span class="keywordflow">return</span> pselect(pcmp_le(y, pset1&lt;T&gt;(5.0)), y_le_five, y_gt_five);</div>
<div class="line"><a name="l01667"></a><span class="lineno"> 1667</span>&#160;  }</div>
<div class="line"><a name="l01668"></a><span class="lineno"> 1668</span>&#160;};</div>
<div class="line"><a name="l01669"></a><span class="lineno"> 1669</span>&#160; </div>
<div class="line"><a name="l01670"></a><span class="lineno"> 1670</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l01671"></a><span class="lineno"> 1671</span>&#160;<span class="keyword">struct </span>bessel_j1_impl {</div>
<div class="line"><a name="l01672"></a><span class="lineno"> 1672</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l01673"></a><span class="lineno"> 1673</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T x) {</div>
<div class="line"><a name="l01674"></a><span class="lineno"> 1674</span>&#160;    <span class="keywordflow">return</span> generic_j1&lt;T&gt;::run(x);</div>
<div class="line"><a name="l01675"></a><span class="lineno"> 1675</span>&#160;  }</div>
<div class="line"><a name="l01676"></a><span class="lineno"> 1676</span>&#160;};</div>
<div class="line"><a name="l01677"></a><span class="lineno"> 1677</span>&#160; </div>
<div class="line"><a name="l01678"></a><span class="lineno"> 1678</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l01679"></a><span class="lineno"> 1679</span>&#160;<span class="keyword">struct </span>bessel_y1_retval {</div>
<div class="line"><a name="l01680"></a><span class="lineno"> 1680</span>&#160;  <span class="keyword">typedef</span> T type;</div>
<div class="line"><a name="l01681"></a><span class="lineno"> 1681</span>&#160;};</div>
<div class="line"><a name="l01682"></a><span class="lineno"> 1682</span>&#160; </div>
<div class="line"><a name="l01683"></a><span class="lineno"> 1683</span>&#160;template &lt;typename T, typename ScalarType = typename unpacket_traits&lt;T&gt;::type&gt;</div>
<div class="line"><a name="l01684"></a><span class="lineno"> 1684</span>&#160;<span class="keyword">struct </span>generic_y1 {</div>
<div class="line"><a name="l01685"></a><span class="lineno"> 1685</span>&#160;  EIGEN_STATIC_ASSERT((internal::is_same&lt;T, T&gt;::value == <span class="keyword">false</span>),</div>
<div class="line"><a name="l01686"></a><span class="lineno"> 1686</span>&#160;                      THIS_TYPE_IS_NOT_SUPPORTED)</div>
<div class="line"><a name="l01687"></a><span class="lineno"> 1687</span>&#160; </div>
<div class="line"><a name="l01688"></a><span class="lineno"> 1688</span>&#160;  EIGEN_DEVICE_FUNC <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp;) {</div>
<div class="line"><a name="l01689"></a><span class="lineno"> 1689</span>&#160;    <span class="keywordflow">return</span> ScalarType(0);</div>
<div class="line"><a name="l01690"></a><span class="lineno"> 1690</span>&#160;  }</div>
<div class="line"><a name="l01691"></a><span class="lineno"> 1691</span>&#160;};</div>
<div class="line"><a name="l01692"></a><span class="lineno"> 1692</span>&#160; </div>
<div class="line"><a name="l01693"></a><span class="lineno"> 1693</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l01694"></a><span class="lineno"> 1694</span>&#160;<span class="keyword">struct </span>generic_y1&lt;T, float&gt; {</div>
<div class="line"><a name="l01695"></a><span class="lineno"> 1695</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l01696"></a><span class="lineno"> 1696</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp; x) {</div>
<div class="line"><a name="l01697"></a><span class="lineno"> 1697</span>&#160;    <span class="comment">/* j1f.c</span></div>
<div class="line"><a name="l01698"></a><span class="lineno"> 1698</span>&#160;<span class="comment">     *  Bessel function of second kind of order one</span></div>
<div class="line"><a name="l01699"></a><span class="lineno"> 1699</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01700"></a><span class="lineno"> 1700</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01701"></a><span class="lineno"> 1701</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01702"></a><span class="lineno"> 1702</span>&#160;<span class="comment">     * SYNOPSIS:</span></div>
<div class="line"><a name="l01703"></a><span class="lineno"> 1703</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01704"></a><span class="lineno"> 1704</span>&#160;<span class="comment">     * double x, y, y1();</span></div>
<div class="line"><a name="l01705"></a><span class="lineno"> 1705</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01706"></a><span class="lineno"> 1706</span>&#160;<span class="comment">     * y = y1( x );</span></div>
<div class="line"><a name="l01707"></a><span class="lineno"> 1707</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01708"></a><span class="lineno"> 1708</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01709"></a><span class="lineno"> 1709</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01710"></a><span class="lineno"> 1710</span>&#160;<span class="comment">     * DESCRIPTION:</span></div>
<div class="line"><a name="l01711"></a><span class="lineno"> 1711</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01712"></a><span class="lineno"> 1712</span>&#160;<span class="comment">     * Returns Bessel function of the second kind of order one</span></div>
<div class="line"><a name="l01713"></a><span class="lineno"> 1713</span>&#160;<span class="comment">     * of the argument.</span></div>
<div class="line"><a name="l01714"></a><span class="lineno"> 1714</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01715"></a><span class="lineno"> 1715</span>&#160;<span class="comment">     * The domain is divided into the intervals [0, 2] and</span></div>
<div class="line"><a name="l01716"></a><span class="lineno"> 1716</span>&#160;<span class="comment">     * (2, infinity). In the first interval a rational approximation</span></div>
<div class="line"><a name="l01717"></a><span class="lineno"> 1717</span>&#160;<span class="comment">     * R(x) is employed to compute</span></div>
<div class="line"><a name="l01718"></a><span class="lineno"> 1718</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01719"></a><span class="lineno"> 1719</span>&#160;<span class="comment">     *                  2</span></div>
<div class="line"><a name="l01720"></a><span class="lineno"> 1720</span>&#160;<span class="comment">     * y0(x)  =  (w - r  ) x R(x^2)  +  2/pi (ln(x) j1(x) - 1/x) .</span></div>
<div class="line"><a name="l01721"></a><span class="lineno"> 1721</span>&#160;<span class="comment">     *                 1</span></div>
<div class="line"><a name="l01722"></a><span class="lineno"> 1722</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01723"></a><span class="lineno"> 1723</span>&#160;<span class="comment">     * Thus a call to j1() is required.</span></div>
<div class="line"><a name="l01724"></a><span class="lineno"> 1724</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01725"></a><span class="lineno"> 1725</span>&#160;<span class="comment">     * In the second interval, the modulus and phase are approximated</span></div>
<div class="line"><a name="l01726"></a><span class="lineno"> 1726</span>&#160;<span class="comment">     * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)</span></div>
<div class="line"><a name="l01727"></a><span class="lineno"> 1727</span>&#160;<span class="comment">     * and Phase(x) = x + 1/x S(1/x^2) - 3pi/4.  Then the function is</span></div>
<div class="line"><a name="l01728"></a><span class="lineno"> 1728</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01729"></a><span class="lineno"> 1729</span>&#160;<span class="comment">     *   y0(x) = Modulus(x) sin( Phase(x) ).</span></div>
<div class="line"><a name="l01730"></a><span class="lineno"> 1730</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01731"></a><span class="lineno"> 1731</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01732"></a><span class="lineno"> 1732</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01733"></a><span class="lineno"> 1733</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01734"></a><span class="lineno"> 1734</span>&#160;<span class="comment">     * ACCURACY:</span></div>
<div class="line"><a name="l01735"></a><span class="lineno"> 1735</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01736"></a><span class="lineno"> 1736</span>&#160;<span class="comment">     *                      Absolute error:</span></div>
<div class="line"><a name="l01737"></a><span class="lineno"> 1737</span>&#160;<span class="comment">     * arithmetic   domain      # trials      peak         rms</span></div>
<div class="line"><a name="l01738"></a><span class="lineno"> 1738</span>&#160;<span class="comment">     *    IEEE      0,  2       100000       2.2e-7     4.6e-8</span></div>
<div class="line"><a name="l01739"></a><span class="lineno"> 1739</span>&#160;<span class="comment">     *    IEEE      2, 32       100000       1.9e-7     5.3e-8</span></div>
<div class="line"><a name="l01740"></a><span class="lineno"> 1740</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01741"></a><span class="lineno"> 1741</span>&#160;<span class="comment">     * (error criterion relative when |y1| &gt; 1).</span></div>
<div class="line"><a name="l01742"></a><span class="lineno"> 1742</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01743"></a><span class="lineno"> 1743</span>&#160;<span class="comment">     */</span></div>
<div class="line"><a name="l01744"></a><span class="lineno"> 1744</span>&#160; </div>
<div class="line"><a name="l01745"></a><span class="lineno"> 1745</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> YP[] = {8.061978323326852E-009f, -9.496460629917016E-007f,</div>
<div class="line"><a name="l01746"></a><span class="lineno"> 1746</span>&#160;                        6.719543806674249E-005f, -2.641785726447862E-003f,</div>
<div class="line"><a name="l01747"></a><span class="lineno"> 1747</span>&#160;                        4.202369946500099E-002f};</div>
<div class="line"><a name="l01748"></a><span class="lineno"> 1748</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> MO1[] = {6.913942741265801E-002f, -2.284801500053359E-001f,</div>
<div class="line"><a name="l01749"></a><span class="lineno"> 1749</span>&#160;                        3.138238455499697E-001f, -2.102302420403875E-001f,</div>
<div class="line"><a name="l01750"></a><span class="lineno"> 1750</span>&#160;                        5.435364690523026E-003f, 1.493389585089498E-001f,</div>
<div class="line"><a name="l01751"></a><span class="lineno"> 1751</span>&#160;                        4.976029650847191E-006f, 7.978845453073848E-001f};</div>
<div class="line"><a name="l01752"></a><span class="lineno"> 1752</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">float</span> PH1[] = {-4.497014141919556E+001f, 5.073465654089319E+001f,</div>
<div class="line"><a name="l01753"></a><span class="lineno"> 1753</span>&#160;                        -2.485774108720340E+001f, 7.222973196770240E+000f,</div>
<div class="line"><a name="l01754"></a><span class="lineno"> 1754</span>&#160;                        -1.544842782180211E+000f, 3.503787691653334E-001f,</div>
<div class="line"><a name="l01755"></a><span class="lineno"> 1755</span>&#160;                        -1.637986776941202E-001f, 3.749989509080821E-001f};</div>
<div class="line"><a name="l01756"></a><span class="lineno"> 1756</span>&#160;    <span class="keyword">const</span> T YO1 = pset1&lt;T&gt;(4.66539330185668857532f);</div>
<div class="line"><a name="l01757"></a><span class="lineno"> 1757</span>&#160;    <span class="keyword">const</span> T NEG_THPIO4F = pset1&lt;T&gt;(-2.35619449019234492885f);    <span class="comment">/* -3*pi/4 */</span></div>
<div class="line"><a name="l01758"></a><span class="lineno"> 1758</span>&#160;    <span class="keyword">const</span> T TWOOPI = pset1&lt;T&gt;(0.636619772367581343075535f); <span class="comment">/* 2/pi */</span></div>
<div class="line"><a name="l01759"></a><span class="lineno"> 1759</span>&#160;    <span class="keyword">const</span> T NEG_MAXNUM = pset1&lt;T&gt;(-NumTraits&lt;float&gt;::infinity());</div>
<div class="line"><a name="l01760"></a><span class="lineno"> 1760</span>&#160; </div>
<div class="line"><a name="l01761"></a><span class="lineno"> 1761</span>&#160;    T z = pmul(x, x);</div>
<div class="line"><a name="l01762"></a><span class="lineno"> 1762</span>&#160;    T x_le_two = pmul(psub(z, YO1), internal::ppolevl&lt;T, 4&gt;::run(z, YP));</div>
<div class="line"><a name="l01763"></a><span class="lineno"> 1763</span>&#160;    x_le_two = pmadd(</div>
<div class="line"><a name="l01764"></a><span class="lineno"> 1764</span>&#160;       x_le_two, x,</div>
<div class="line"><a name="l01765"></a><span class="lineno"> 1765</span>&#160;       pmul(TWOOPI, pmadd(</div>
<div class="line"><a name="l01766"></a><span class="lineno"> 1766</span>&#160;           generic_j1&lt;T, float&gt;::run(x), plog(x),</div>
<div class="line"><a name="l01767"></a><span class="lineno"> 1767</span>&#160;           pdiv(pset1&lt;T&gt;(-1.0f), x))));</div>
<div class="line"><a name="l01768"></a><span class="lineno"> 1768</span>&#160;    x_le_two = pselect(pcmp_lt(x, pset1&lt;T&gt;(0.0f)), NEG_MAXNUM, x_le_two);</div>
<div class="line"><a name="l01769"></a><span class="lineno"> 1769</span>&#160; </div>
<div class="line"><a name="l01770"></a><span class="lineno"> 1770</span>&#160;    T q = pdiv(pset1&lt;T&gt;(1.0), x);</div>
<div class="line"><a name="l01771"></a><span class="lineno"> 1771</span>&#160;    T w = prsqrt(x);</div>
<div class="line"><a name="l01772"></a><span class="lineno"> 1772</span>&#160;    T p = pmul(w, internal::ppolevl&lt;T, 7&gt;::run(q, MO1));</div>
<div class="line"><a name="l01773"></a><span class="lineno"> 1773</span>&#160;    w = pmul(q, q);</div>
<div class="line"><a name="l01774"></a><span class="lineno"> 1774</span>&#160;    T xn = pmadd(q, internal::ppolevl&lt;T, 7&gt;::run(w, PH1), NEG_THPIO4F);</div>
<div class="line"><a name="l01775"></a><span class="lineno"> 1775</span>&#160;    T x_gt_two = pmul(p, psin(padd(xn, x)));</div>
<div class="line"><a name="l01776"></a><span class="lineno"> 1776</span>&#160;    <span class="keywordflow">return</span> pselect(pcmp_le(x, pset1&lt;T&gt;(2.0)), x_le_two, x_gt_two);</div>
<div class="line"><a name="l01777"></a><span class="lineno"> 1777</span>&#160;  }</div>
<div class="line"><a name="l01778"></a><span class="lineno"> 1778</span>&#160;};</div>
<div class="line"><a name="l01779"></a><span class="lineno"> 1779</span>&#160; </div>
<div class="line"><a name="l01780"></a><span class="lineno"> 1780</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l01781"></a><span class="lineno"> 1781</span>&#160;<span class="keyword">struct </span>generic_y1&lt;T, double&gt; {</div>
<div class="line"><a name="l01782"></a><span class="lineno"> 1782</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l01783"></a><span class="lineno"> 1783</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T&amp; x) {</div>
<div class="line"><a name="l01784"></a><span class="lineno"> 1784</span>&#160;    <span class="comment">/*  j1.c</span></div>
<div class="line"><a name="l01785"></a><span class="lineno"> 1785</span>&#160;<span class="comment">     *  Bessel function of second kind of order one</span></div>
<div class="line"><a name="l01786"></a><span class="lineno"> 1786</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01787"></a><span class="lineno"> 1787</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01788"></a><span class="lineno"> 1788</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01789"></a><span class="lineno"> 1789</span>&#160;<span class="comment">     * SYNOPSIS:</span></div>
<div class="line"><a name="l01790"></a><span class="lineno"> 1790</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01791"></a><span class="lineno"> 1791</span>&#160;<span class="comment">     * double x, y, y1();</span></div>
<div class="line"><a name="l01792"></a><span class="lineno"> 1792</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01793"></a><span class="lineno"> 1793</span>&#160;<span class="comment">     * y = y1( x );</span></div>
<div class="line"><a name="l01794"></a><span class="lineno"> 1794</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01795"></a><span class="lineno"> 1795</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01796"></a><span class="lineno"> 1796</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01797"></a><span class="lineno"> 1797</span>&#160;<span class="comment">     * DESCRIPTION:</span></div>
<div class="line"><a name="l01798"></a><span class="lineno"> 1798</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01799"></a><span class="lineno"> 1799</span>&#160;<span class="comment">     * Returns Bessel function of the second kind of order one</span></div>
<div class="line"><a name="l01800"></a><span class="lineno"> 1800</span>&#160;<span class="comment">     * of the argument.</span></div>
<div class="line"><a name="l01801"></a><span class="lineno"> 1801</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01802"></a><span class="lineno"> 1802</span>&#160;<span class="comment">     * The domain is divided into the intervals [0, 8] and</span></div>
<div class="line"><a name="l01803"></a><span class="lineno"> 1803</span>&#160;<span class="comment">     * (8, infinity). In the first interval a 25 term Chebyshev</span></div>
<div class="line"><a name="l01804"></a><span class="lineno"> 1804</span>&#160;<span class="comment">     * expansion is used, and a call to j1() is required.</span></div>
<div class="line"><a name="l01805"></a><span class="lineno"> 1805</span>&#160;<span class="comment">     * In the second, the asymptotic trigonometric representation</span></div>
<div class="line"><a name="l01806"></a><span class="lineno"> 1806</span>&#160;<span class="comment">     * is employed using two rational functions of degree 5/5.</span></div>
<div class="line"><a name="l01807"></a><span class="lineno"> 1807</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01808"></a><span class="lineno"> 1808</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01809"></a><span class="lineno"> 1809</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01810"></a><span class="lineno"> 1810</span>&#160;<span class="comment">     * ACCURACY:</span></div>
<div class="line"><a name="l01811"></a><span class="lineno"> 1811</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01812"></a><span class="lineno"> 1812</span>&#160;<span class="comment">     *                      Absolute error:</span></div>
<div class="line"><a name="l01813"></a><span class="lineno"> 1813</span>&#160;<span class="comment">     * arithmetic   domain      # trials      peak         rms</span></div>
<div class="line"><a name="l01814"></a><span class="lineno"> 1814</span>&#160;<span class="comment">     *    DEC       0, 30       10000       8.6e-17     1.3e-17</span></div>
<div class="line"><a name="l01815"></a><span class="lineno"> 1815</span>&#160;<span class="comment">     *    IEEE      0, 30       30000       1.0e-15     1.3e-16</span></div>
<div class="line"><a name="l01816"></a><span class="lineno"> 1816</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01817"></a><span class="lineno"> 1817</span>&#160;<span class="comment">     * (error criterion relative when |y1| &gt; 1).</span></div>
<div class="line"><a name="l01818"></a><span class="lineno"> 1818</span>&#160;<span class="comment">     *</span></div>
<div class="line"><a name="l01819"></a><span class="lineno"> 1819</span>&#160;<span class="comment">     */</span></div>
<div class="line"><a name="l01820"></a><span class="lineno"> 1820</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> PP[] = {7.62125616208173112003E-4, 7.31397056940917570436E-2,</div>
<div class="line"><a name="l01821"></a><span class="lineno"> 1821</span>&#160;                         1.12719608129684925192E0, 5.11207951146807644818E0,</div>
<div class="line"><a name="l01822"></a><span class="lineno"> 1822</span>&#160;                         8.42404590141772420927E0, 5.21451598682361504063E0,</div>
<div class="line"><a name="l01823"></a><span class="lineno"> 1823</span>&#160;                         1.00000000000000000254E0};</div>
<div class="line"><a name="l01824"></a><span class="lineno"> 1824</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> PQ[] = {5.71323128072548699714E-4, 6.88455908754495404082E-2,</div>
<div class="line"><a name="l01825"></a><span class="lineno"> 1825</span>&#160;                         1.10514232634061696926E0, 5.07386386128601488557E0,</div>
<div class="line"><a name="l01826"></a><span class="lineno"> 1826</span>&#160;                         8.39985554327604159757E0, 5.20982848682361821619E0,</div>
<div class="line"><a name="l01827"></a><span class="lineno"> 1827</span>&#160;                         9.99999999999999997461E-1};</div>
<div class="line"><a name="l01828"></a><span class="lineno"> 1828</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> QP[] = {5.10862594750176621635E-2, 4.98213872951233449420E0,</div>
<div class="line"><a name="l01829"></a><span class="lineno"> 1829</span>&#160;                         7.58238284132545283818E1, 3.66779609360150777800E2,</div>
<div class="line"><a name="l01830"></a><span class="lineno"> 1830</span>&#160;                         7.10856304998926107277E2, 5.97489612400613639965E2,</div>
<div class="line"><a name="l01831"></a><span class="lineno"> 1831</span>&#160;                         2.11688757100572135698E2, 2.52070205858023719784E1};</div>
<div class="line"><a name="l01832"></a><span class="lineno"> 1832</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> QQ[] = {1.00000000000000000000E0, 7.42373277035675149943E1,</div>
<div class="line"><a name="l01833"></a><span class="lineno"> 1833</span>&#160;                         1.05644886038262816351E3, 4.98641058337653607651E3,</div>
<div class="line"><a name="l01834"></a><span class="lineno"> 1834</span>&#160;                         9.56231892404756170795E3, 7.99704160447350683650E3,</div>
<div class="line"><a name="l01835"></a><span class="lineno"> 1835</span>&#160;                         2.82619278517639096600E3, 3.36093607810698293419E2};</div>
<div class="line"><a name="l01836"></a><span class="lineno"> 1836</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> YP[] = {1.26320474790178026440E9, -6.47355876379160291031E11,</div>
<div class="line"><a name="l01837"></a><span class="lineno"> 1837</span>&#160;                         1.14509511541823727583E14, -8.12770255501325109621E15,</div>
<div class="line"><a name="l01838"></a><span class="lineno"> 1838</span>&#160;                         2.02439475713594898196E17, -7.78877196265950026825E17};</div>
<div class="line"><a name="l01839"></a><span class="lineno"> 1839</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">double</span> YQ[] = {1.00000000000000000000E0, 5.94301592346128195359E2,</div>
<div class="line"><a name="l01840"></a><span class="lineno"> 1840</span>&#160;                         2.35564092943068577943E5, 7.34811944459721705660E7,</div>
<div class="line"><a name="l01841"></a><span class="lineno"> 1841</span>&#160;                         1.87601316108706159478E10, 3.88231277496238566008E12,</div>
<div class="line"><a name="l01842"></a><span class="lineno"> 1842</span>&#160;                         6.20557727146953693363E14, 6.87141087355300489866E16,</div>
<div class="line"><a name="l01843"></a><span class="lineno"> 1843</span>&#160;                         3.97270608116560655612E18};</div>
<div class="line"><a name="l01844"></a><span class="lineno"> 1844</span>&#160;    <span class="keyword">const</span> T SQ2OPI = pset1&lt;T&gt;(.79788456080286535588);</div>
<div class="line"><a name="l01845"></a><span class="lineno"> 1845</span>&#160;    <span class="keyword">const</span> T NEG_THPIO4 = pset1&lt;T&gt;(-2.35619449019234492885);    <span class="comment">/* -3*pi/4 */</span></div>
<div class="line"><a name="l01846"></a><span class="lineno"> 1846</span>&#160;    <span class="keyword">const</span> T TWOOPI = pset1&lt;T&gt;(0.636619772367581343075535); <span class="comment">/* 2/pi */</span></div>
<div class="line"><a name="l01847"></a><span class="lineno"> 1847</span>&#160;    <span class="keyword">const</span> T NEG_MAXNUM = pset1&lt;T&gt;(-NumTraits&lt;double&gt;::infinity());</div>
<div class="line"><a name="l01848"></a><span class="lineno"> 1848</span>&#160; </div>
<div class="line"><a name="l01849"></a><span class="lineno"> 1849</span>&#160;    T z = pmul(x, x);</div>
<div class="line"><a name="l01850"></a><span class="lineno"> 1850</span>&#160;    T x_le_five = pdiv(internal::ppolevl&lt;T, 5&gt;::run(z, YP),</div>
<div class="line"><a name="l01851"></a><span class="lineno"> 1851</span>&#160;                   internal::ppolevl&lt;T, 8&gt;::run(z, YQ));</div>
<div class="line"><a name="l01852"></a><span class="lineno"> 1852</span>&#160;    x_le_five = pmadd(</div>
<div class="line"><a name="l01853"></a><span class="lineno"> 1853</span>&#160;        x_le_five, x, pmul(</div>
<div class="line"><a name="l01854"></a><span class="lineno"> 1854</span>&#160;            TWOOPI, pmadd(generic_j1&lt;T, double&gt;::run(x), plog(x),</div>
<div class="line"><a name="l01855"></a><span class="lineno"> 1855</span>&#160;                          pdiv(pset1&lt;T&gt;(-1.0), x))));</div>
<div class="line"><a name="l01856"></a><span class="lineno"> 1856</span>&#160; </div>
<div class="line"><a name="l01857"></a><span class="lineno"> 1857</span>&#160;    x_le_five = pselect(pcmp_le(x, pset1&lt;T&gt;(0.0)), NEG_MAXNUM, x_le_five);</div>
<div class="line"><a name="l01858"></a><span class="lineno"> 1858</span>&#160;    T s = pdiv(pset1&lt;T&gt;(25.0), z);</div>
<div class="line"><a name="l01859"></a><span class="lineno"> 1859</span>&#160;    T p = pdiv(</div>
<div class="line"><a name="l01860"></a><span class="lineno"> 1860</span>&#160;        internal::ppolevl&lt;T, 6&gt;::run(s, PP),</div>
<div class="line"><a name="l01861"></a><span class="lineno"> 1861</span>&#160;        internal::ppolevl&lt;T, 6&gt;::run(s, PQ));</div>
<div class="line"><a name="l01862"></a><span class="lineno"> 1862</span>&#160;    T q = pdiv(</div>
<div class="line"><a name="l01863"></a><span class="lineno"> 1863</span>&#160;        internal::ppolevl&lt;T, 7&gt;::run(s, QP),</div>
<div class="line"><a name="l01864"></a><span class="lineno"> 1864</span>&#160;        internal::ppolevl&lt;T, 7&gt;::run(s, QQ));</div>
<div class="line"><a name="l01865"></a><span class="lineno"> 1865</span>&#160;    T xn = padd(x, NEG_THPIO4);</div>
<div class="line"><a name="l01866"></a><span class="lineno"> 1866</span>&#160;    T w = pdiv(pset1&lt;T&gt;(5.0), x);</div>
<div class="line"><a name="l01867"></a><span class="lineno"> 1867</span>&#160;    p = pmadd(p, psin(xn), pmul(w, pmul(q, pcos(xn))));</div>
<div class="line"><a name="l01868"></a><span class="lineno"> 1868</span>&#160;    T x_gt_five = pmul(p, pmul(SQ2OPI, prsqrt(x)));</div>
<div class="line"><a name="l01869"></a><span class="lineno"> 1869</span>&#160;    <span class="keywordflow">return</span> pselect(pcmp_le(x, pset1&lt;T&gt;(5.0)), x_le_five, x_gt_five);</div>
<div class="line"><a name="l01870"></a><span class="lineno"> 1870</span>&#160;  }</div>
<div class="line"><a name="l01871"></a><span class="lineno"> 1871</span>&#160;};</div>
<div class="line"><a name="l01872"></a><span class="lineno"> 1872</span>&#160; </div>
<div class="line"><a name="l01873"></a><span class="lineno"> 1873</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l01874"></a><span class="lineno"> 1874</span>&#160;<span class="keyword">struct </span>bessel_y1_impl {</div>
<div class="line"><a name="l01875"></a><span class="lineno"> 1875</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l01876"></a><span class="lineno"> 1876</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE T run(<span class="keyword">const</span> T x) {</div>
<div class="line"><a name="l01877"></a><span class="lineno"> 1877</span>&#160;    <span class="keywordflow">return</span> generic_y1&lt;T&gt;::run(x);</div>
<div class="line"><a name="l01878"></a><span class="lineno"> 1878</span>&#160;  }</div>
<div class="line"><a name="l01879"></a><span class="lineno"> 1879</span>&#160;};</div>
<div class="line"><a name="l01880"></a><span class="lineno"> 1880</span>&#160; </div>
<div class="line"><a name="l01881"></a><span class="lineno"> 1881</span>&#160;}  <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l01882"></a><span class="lineno"> 1882</span>&#160; </div>
<div class="line"><a name="l01883"></a><span class="lineno"> 1883</span>&#160;<span class="keyword">namespace </span>numext {</div>
<div class="line"><a name="l01884"></a><span class="lineno"> 1884</span>&#160; </div>
<div class="line"><a name="l01885"></a><span class="lineno"> 1885</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar&gt;</div>
<div class="line"><a name="l01886"></a><span class="lineno"> 1886</span>&#160;EIGEN_DEVICE_FUNC <span class="keyword">inline</span> EIGEN_MATHFUNC_RETVAL(<a class="code" href="namespaceEigen.html#ab0c429bb38ce58964b561fb9d6c9377a">bessel_i0</a>, Scalar)</div>
<div class="line"><a name="l01887"></a><span class="lineno"> 1887</span>&#160;    <a class="code" href="namespaceEigen.html#ab0c429bb38ce58964b561fb9d6c9377a">bessel_i0</a>(<span class="keyword">const</span> Scalar&amp; x) {</div>
<div class="line"><a name="l01888"></a><span class="lineno"> 1888</span>&#160;  <span class="keywordflow">return</span> EIGEN_MATHFUNC_IMPL(<a class="code" href="namespaceEigen.html#ab0c429bb38ce58964b561fb9d6c9377a">bessel_i0</a>, Scalar)::run(x);</div>
<div class="line"><a name="l01889"></a><span class="lineno"> 1889</span>&#160;}</div>
<div class="line"><a name="l01890"></a><span class="lineno"> 1890</span>&#160; </div>
<div class="line"><a name="l01891"></a><span class="lineno"> 1891</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar&gt;</div>
<div class="line"><a name="l01892"></a><span class="lineno"> 1892</span>&#160;EIGEN_DEVICE_FUNC <span class="keyword">inline</span> EIGEN_MATHFUNC_RETVAL(<a class="code" href="namespaceEigen.html#aef13ab56dea757bfb7bd3e220ac478d5">bessel_i0e</a>, Scalar)</div>
<div class="line"><a name="l01893"></a><span class="lineno"> 1893</span>&#160;    <a class="code" href="namespaceEigen.html#aef13ab56dea757bfb7bd3e220ac478d5">bessel_i0e</a>(<span class="keyword">const</span> Scalar&amp; x) {</div>
<div class="line"><a name="l01894"></a><span class="lineno"> 1894</span>&#160;  <span class="keywordflow">return</span> EIGEN_MATHFUNC_IMPL(<a class="code" href="namespaceEigen.html#aef13ab56dea757bfb7bd3e220ac478d5">bessel_i0e</a>, Scalar)::run(x);</div>
<div class="line"><a name="l01895"></a><span class="lineno"> 1895</span>&#160;}</div>
<div class="line"><a name="l01896"></a><span class="lineno"> 1896</span>&#160; </div>
<div class="line"><a name="l01897"></a><span class="lineno"> 1897</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar&gt;</div>
<div class="line"><a name="l01898"></a><span class="lineno"> 1898</span>&#160;EIGEN_DEVICE_FUNC <span class="keyword">inline</span> EIGEN_MATHFUNC_RETVAL(<a class="code" href="namespaceEigen.html#ae35e1cabdc81f3783219186a7e658a2b">bessel_i1</a>, Scalar)</div>
<div class="line"><a name="l01899"></a><span class="lineno"> 1899</span>&#160;    <a class="code" href="namespaceEigen.html#ae35e1cabdc81f3783219186a7e658a2b">bessel_i1</a>(<span class="keyword">const</span> Scalar&amp; x) {</div>
<div class="line"><a name="l01900"></a><span class="lineno"> 1900</span>&#160;  <span class="keywordflow">return</span> EIGEN_MATHFUNC_IMPL(<a class="code" href="namespaceEigen.html#ae35e1cabdc81f3783219186a7e658a2b">bessel_i1</a>, Scalar)::run(x);</div>
<div class="line"><a name="l01901"></a><span class="lineno"> 1901</span>&#160;}</div>
<div class="line"><a name="l01902"></a><span class="lineno"> 1902</span>&#160; </div>
<div class="line"><a name="l01903"></a><span class="lineno"> 1903</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar&gt;</div>
<div class="line"><a name="l01904"></a><span class="lineno"> 1904</span>&#160;EIGEN_DEVICE_FUNC <span class="keyword">inline</span> EIGEN_MATHFUNC_RETVAL(<a class="code" href="namespaceEigen.html#ae52c524c4108c6265e9543468da42e28">bessel_i1e</a>, Scalar)</div>
<div class="line"><a name="l01905"></a><span class="lineno"> 1905</span>&#160;    <a class="code" href="namespaceEigen.html#ae52c524c4108c6265e9543468da42e28">bessel_i1e</a>(<span class="keyword">const</span> Scalar&amp; x) {</div>
<div class="line"><a name="l01906"></a><span class="lineno"> 1906</span>&#160;  <span class="keywordflow">return</span> EIGEN_MATHFUNC_IMPL(<a class="code" href="namespaceEigen.html#ae52c524c4108c6265e9543468da42e28">bessel_i1e</a>, Scalar)::run(x);</div>
<div class="line"><a name="l01907"></a><span class="lineno"> 1907</span>&#160;}</div>
<div class="line"><a name="l01908"></a><span class="lineno"> 1908</span>&#160; </div>
<div class="line"><a name="l01909"></a><span class="lineno"> 1909</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar&gt;</div>
<div class="line"><a name="l01910"></a><span class="lineno"> 1910</span>&#160;EIGEN_DEVICE_FUNC <span class="keyword">inline</span> EIGEN_MATHFUNC_RETVAL(<a class="code" href="namespaceEigen.html#a4664123a5ae23d981410d7dc5cd86970">bessel_k0</a>, Scalar)</div>
<div class="line"><a name="l01911"></a><span class="lineno"> 1911</span>&#160;    <a class="code" href="namespaceEigen.html#a4664123a5ae23d981410d7dc5cd86970">bessel_k0</a>(<span class="keyword">const</span> Scalar&amp; x) {</div>
<div class="line"><a name="l01912"></a><span class="lineno"> 1912</span>&#160;  <span class="keywordflow">return</span> EIGEN_MATHFUNC_IMPL(<a class="code" href="namespaceEigen.html#a4664123a5ae23d981410d7dc5cd86970">bessel_k0</a>, Scalar)::run(x);</div>
<div class="line"><a name="l01913"></a><span class="lineno"> 1913</span>&#160;}</div>
<div class="line"><a name="l01914"></a><span class="lineno"> 1914</span>&#160; </div>
<div class="line"><a name="l01915"></a><span class="lineno"> 1915</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar&gt;</div>
<div class="line"><a name="l01916"></a><span class="lineno"> 1916</span>&#160;EIGEN_DEVICE_FUNC <span class="keyword">inline</span> EIGEN_MATHFUNC_RETVAL(<a class="code" href="namespaceEigen.html#a9cc57448af6eda4fa72f34be7cc72da5">bessel_k0e</a>, Scalar)</div>
<div class="line"><a name="l01917"></a><span class="lineno"> 1917</span>&#160;    <a class="code" href="namespaceEigen.html#a9cc57448af6eda4fa72f34be7cc72da5">bessel_k0e</a>(<span class="keyword">const</span> Scalar&amp; x) {</div>
<div class="line"><a name="l01918"></a><span class="lineno"> 1918</span>&#160;  <span class="keywordflow">return</span> EIGEN_MATHFUNC_IMPL(<a class="code" href="namespaceEigen.html#a9cc57448af6eda4fa72f34be7cc72da5">bessel_k0e</a>, Scalar)::run(x);</div>
<div class="line"><a name="l01919"></a><span class="lineno"> 1919</span>&#160;}</div>
<div class="line"><a name="l01920"></a><span class="lineno"> 1920</span>&#160; </div>
<div class="line"><a name="l01921"></a><span class="lineno"> 1921</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar&gt;</div>
<div class="line"><a name="l01922"></a><span class="lineno"> 1922</span>&#160;EIGEN_DEVICE_FUNC <span class="keyword">inline</span> EIGEN_MATHFUNC_RETVAL(<a class="code" href="namespaceEigen.html#a76e76fa84ed24785bf32665a48157bf1">bessel_k1</a>, Scalar)</div>
<div class="line"><a name="l01923"></a><span class="lineno"> 1923</span>&#160;    <a class="code" href="namespaceEigen.html#a76e76fa84ed24785bf32665a48157bf1">bessel_k1</a>(<span class="keyword">const</span> Scalar&amp; x) {</div>
<div class="line"><a name="l01924"></a><span class="lineno"> 1924</span>&#160;  <span class="keywordflow">return</span> EIGEN_MATHFUNC_IMPL(<a class="code" href="namespaceEigen.html#a76e76fa84ed24785bf32665a48157bf1">bessel_k1</a>, Scalar)::run(x);</div>
<div class="line"><a name="l01925"></a><span class="lineno"> 1925</span>&#160;}</div>
<div class="line"><a name="l01926"></a><span class="lineno"> 1926</span>&#160; </div>
<div class="line"><a name="l01927"></a><span class="lineno"> 1927</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar&gt;</div>
<div class="line"><a name="l01928"></a><span class="lineno"> 1928</span>&#160;EIGEN_DEVICE_FUNC <span class="keyword">inline</span> EIGEN_MATHFUNC_RETVAL(<a class="code" href="namespaceEigen.html#af9e044c2baa913adea597c4d497a3315">bessel_k1e</a>, Scalar)</div>
<div class="line"><a name="l01929"></a><span class="lineno"> 1929</span>&#160;    <a class="code" href="namespaceEigen.html#af9e044c2baa913adea597c4d497a3315">bessel_k1e</a>(<span class="keyword">const</span> Scalar&amp; x) {</div>
<div class="line"><a name="l01930"></a><span class="lineno"> 1930</span>&#160;  <span class="keywordflow">return</span> EIGEN_MATHFUNC_IMPL(<a class="code" href="namespaceEigen.html#af9e044c2baa913adea597c4d497a3315">bessel_k1e</a>, Scalar)::run(x);</div>
<div class="line"><a name="l01931"></a><span class="lineno"> 1931</span>&#160;}</div>
<div class="line"><a name="l01932"></a><span class="lineno"> 1932</span>&#160; </div>
<div class="line"><a name="l01933"></a><span class="lineno"> 1933</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar&gt;</div>
<div class="line"><a name="l01934"></a><span class="lineno"> 1934</span>&#160;EIGEN_DEVICE_FUNC <span class="keyword">inline</span> EIGEN_MATHFUNC_RETVAL(<a class="code" href="namespaceEigen.html#a65acfc33a2b6140a09af67e45928e037">bessel_j0</a>, Scalar)</div>
<div class="line"><a name="l01935"></a><span class="lineno"> 1935</span>&#160;    <a class="code" href="namespaceEigen.html#a65acfc33a2b6140a09af67e45928e037">bessel_j0</a>(<span class="keyword">const</span> Scalar&amp; x) {</div>
<div class="line"><a name="l01936"></a><span class="lineno"> 1936</span>&#160;  <span class="keywordflow">return</span> EIGEN_MATHFUNC_IMPL(<a class="code" href="namespaceEigen.html#a65acfc33a2b6140a09af67e45928e037">bessel_j0</a>, Scalar)::run(x);</div>
<div class="line"><a name="l01937"></a><span class="lineno"> 1937</span>&#160;}</div>
<div class="line"><a name="l01938"></a><span class="lineno"> 1938</span>&#160; </div>
<div class="line"><a name="l01939"></a><span class="lineno"> 1939</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar&gt;</div>
<div class="line"><a name="l01940"></a><span class="lineno"> 1940</span>&#160;EIGEN_DEVICE_FUNC <span class="keyword">inline</span> EIGEN_MATHFUNC_RETVAL(<a class="code" href="namespaceEigen.html#aad0c42bfd8d5b4169a542206b460b2d0">bessel_y0</a>, Scalar)</div>
<div class="line"><a name="l01941"></a><span class="lineno"> 1941</span>&#160;    <a class="code" href="namespaceEigen.html#aad0c42bfd8d5b4169a542206b460b2d0">bessel_y0</a>(<span class="keyword">const</span> Scalar&amp; x) {</div>
<div class="line"><a name="l01942"></a><span class="lineno"> 1942</span>&#160;  <span class="keywordflow">return</span> EIGEN_MATHFUNC_IMPL(<a class="code" href="namespaceEigen.html#aad0c42bfd8d5b4169a542206b460b2d0">bessel_y0</a>, Scalar)::run(x);</div>
<div class="line"><a name="l01943"></a><span class="lineno"> 1943</span>&#160;}</div>
<div class="line"><a name="l01944"></a><span class="lineno"> 1944</span>&#160; </div>
<div class="line"><a name="l01945"></a><span class="lineno"> 1945</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar&gt;</div>
<div class="line"><a name="l01946"></a><span class="lineno"> 1946</span>&#160;EIGEN_DEVICE_FUNC <span class="keyword">inline</span> EIGEN_MATHFUNC_RETVAL(<a class="code" href="namespaceEigen.html#a4079ddbfe44e3a865cdb600353f371ab">bessel_j1</a>, Scalar)</div>
<div class="line"><a name="l01947"></a><span class="lineno"> 1947</span>&#160;    <a class="code" href="namespaceEigen.html#a4079ddbfe44e3a865cdb600353f371ab">bessel_j1</a>(<span class="keyword">const</span> Scalar&amp; x) {</div>
<div class="line"><a name="l01948"></a><span class="lineno"> 1948</span>&#160;  <span class="keywordflow">return</span> EIGEN_MATHFUNC_IMPL(<a class="code" href="namespaceEigen.html#a4079ddbfe44e3a865cdb600353f371ab">bessel_j1</a>, Scalar)::run(x);</div>
<div class="line"><a name="l01949"></a><span class="lineno"> 1949</span>&#160;}</div>
<div class="line"><a name="l01950"></a><span class="lineno"> 1950</span>&#160; </div>
<div class="line"><a name="l01951"></a><span class="lineno"> 1951</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar&gt;</div>
<div class="line"><a name="l01952"></a><span class="lineno"> 1952</span>&#160;EIGEN_DEVICE_FUNC <span class="keyword">inline</span> EIGEN_MATHFUNC_RETVAL(<a class="code" href="namespaceEigen.html#a60d76185793d52703fa01d83d5b46615">bessel_y1</a>, Scalar)</div>
<div class="line"><a name="l01953"></a><span class="lineno"> 1953</span>&#160;    <a class="code" href="namespaceEigen.html#a60d76185793d52703fa01d83d5b46615">bessel_y1</a>(<span class="keyword">const</span> Scalar&amp; x) {</div>
<div class="line"><a name="l01954"></a><span class="lineno"> 1954</span>&#160;  <span class="keywordflow">return</span> EIGEN_MATHFUNC_IMPL(<a class="code" href="namespaceEigen.html#a60d76185793d52703fa01d83d5b46615">bessel_y1</a>, Scalar)::run(x);</div>
<div class="line"><a name="l01955"></a><span class="lineno"> 1955</span>&#160;}</div>
<div class="line"><a name="l01956"></a><span class="lineno"> 1956</span>&#160; </div>
<div class="line"><a name="l01957"></a><span class="lineno"> 1957</span>&#160;}  <span class="comment">// end namespace numext</span></div>
<div class="line"><a name="l01958"></a><span class="lineno"> 1958</span>&#160; </div>
<div class="line"><a name="l01959"></a><span class="lineno"> 1959</span>&#160;}  <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l01960"></a><span class="lineno"> 1960</span>&#160; </div>
<div class="line"><a name="l01961"></a><span class="lineno"> 1961</span>&#160;<span class="preprocessor">#endif  </span><span class="comment">// EIGEN_BESSEL_FUNCTIONS_H</span></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div></div>
<div class="ttc" id="anamespaceEigen_html_a4079ddbfe44e3a865cdb600353f371ab"><div class="ttname"><a href="namespaceEigen.html#a4079ddbfe44e3a865cdb600353f371ab">Eigen::bessel_j1</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_bessel_j1_op&lt; typename Derived::Scalar &gt;, const Derived &gt; bessel_j1(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div><div class="ttdef"><b>Definition:</b> BesselFunctionsArrayAPI.h:258</div></div>
<div class="ttc" id="anamespaceEigen_html_a4664123a5ae23d981410d7dc5cd86970"><div class="ttname"><a href="namespaceEigen.html#a4664123a5ae23d981410d7dc5cd86970">Eigen::bessel_k0</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_bessel_k0_op&lt; typename Derived::Scalar &gt;, const Derived &gt; bessel_k0(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div><div class="ttdef"><b>Definition:</b> BesselFunctionsArrayAPI.h:124</div></div>
<div class="ttc" id="anamespaceEigen_html_a60d76185793d52703fa01d83d5b46615"><div class="ttname"><a href="namespaceEigen.html#a60d76185793d52703fa01d83d5b46615">Eigen::bessel_y1</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_bessel_y1_op&lt; typename Derived::Scalar &gt;, const Derived &gt; bessel_y1(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div><div class="ttdef"><b>Definition:</b> BesselFunctionsArrayAPI.h:280</div></div>
<div class="ttc" id="anamespaceEigen_html_a65acfc33a2b6140a09af67e45928e037"><div class="ttname"><a href="namespaceEigen.html#a65acfc33a2b6140a09af67e45928e037">Eigen::bessel_j0</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_bessel_j0_op&lt; typename Derived::Scalar &gt;, const Derived &gt; bessel_j0(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div><div class="ttdef"><b>Definition:</b> BesselFunctionsArrayAPI.h:214</div></div>
<div class="ttc" id="anamespaceEigen_html_a76e76fa84ed24785bf32665a48157bf1"><div class="ttname"><a href="namespaceEigen.html#a76e76fa84ed24785bf32665a48157bf1">Eigen::bessel_k1</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_bessel_k1_op&lt; typename Derived::Scalar &gt;, const Derived &gt; bessel_k1(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div><div class="ttdef"><b>Definition:</b> BesselFunctionsArrayAPI.h:169</div></div>
<div class="ttc" id="anamespaceEigen_html_a9cc57448af6eda4fa72f34be7cc72da5"><div class="ttname"><a href="namespaceEigen.html#a9cc57448af6eda4fa72f34be7cc72da5">Eigen::bessel_k0e</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_bessel_k0e_op&lt; typename Derived::Scalar &gt;, const Derived &gt; bessel_k0e(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div><div class="ttdef"><b>Definition:</b> BesselFunctionsArrayAPI.h:147</div></div>
<div class="ttc" id="anamespaceEigen_html_aad0c42bfd8d5b4169a542206b460b2d0"><div class="ttname"><a href="namespaceEigen.html#aad0c42bfd8d5b4169a542206b460b2d0">Eigen::bessel_y0</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_bessel_y0_op&lt; typename Derived::Scalar &gt;, const Derived &gt; bessel_y0(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div><div class="ttdef"><b>Definition:</b> BesselFunctionsArrayAPI.h:236</div></div>
<div class="ttc" id="anamespaceEigen_html_ab0c429bb38ce58964b561fb9d6c9377a"><div class="ttname"><a href="namespaceEigen.html#ab0c429bb38ce58964b561fb9d6c9377a">Eigen::bessel_i0</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_bessel_i0_op&lt; typename Derived::Scalar &gt;, const Derived &gt; bessel_i0(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div><div class="ttdef"><b>Definition:</b> BesselFunctionsArrayAPI.h:34</div></div>
<div class="ttc" id="anamespaceEigen_html_ae35e1cabdc81f3783219186a7e658a2b"><div class="ttname"><a href="namespaceEigen.html#ae35e1cabdc81f3783219186a7e658a2b">Eigen::bessel_i1</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_bessel_i1_op&lt; typename Derived::Scalar &gt;, const Derived &gt; bessel_i1(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div><div class="ttdef"><b>Definition:</b> BesselFunctionsArrayAPI.h:79</div></div>
<div class="ttc" id="anamespaceEigen_html_ae52c524c4108c6265e9543468da42e28"><div class="ttname"><a href="namespaceEigen.html#ae52c524c4108c6265e9543468da42e28">Eigen::bessel_i1e</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_bessel_i1e_op&lt; typename Derived::Scalar &gt;, const Derived &gt; bessel_i1e(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div><div class="ttdef"><b>Definition:</b> BesselFunctionsArrayAPI.h:102</div></div>
<div class="ttc" id="anamespaceEigen_html_aef13ab56dea757bfb7bd3e220ac478d5"><div class="ttname"><a href="namespaceEigen.html#aef13ab56dea757bfb7bd3e220ac478d5">Eigen::bessel_i0e</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_bessel_i0e_op&lt; typename Derived::Scalar &gt;, const Derived &gt; bessel_i0e(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div><div class="ttdef"><b>Definition:</b> BesselFunctionsArrayAPI.h:57</div></div>
<div class="ttc" id="anamespaceEigen_html_af9e044c2baa913adea597c4d497a3315"><div class="ttname"><a href="namespaceEigen.html#af9e044c2baa913adea597c4d497a3315">Eigen::bessel_k1e</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_bessel_k1e_op&lt; typename Derived::Scalar &gt;, const Derived &gt; bessel_k1e(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div><div class="ttdef"><b>Definition:</b> BesselFunctionsArrayAPI.h:192</div></div>
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